Pain of Quadratics (HTML) (General Discussion)

Pain of Quadratics (HTML) // General Discussion

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strike rapier

Sep 3, 2003, 3:10pm
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This is the very description of pain.. and its in HTML because I require =
a fixed width font >:)

Simplify:

[ 2x^2 + x - 1 2x^2 - 5x + 3 ] [6x^2 + x - 2 ]
[ ------------ X ------------- ] / [-------------]
[ x^2 - 1 2x^2 - 7x + 3 ] [3x^2 - 7x - 6]

Now according to my maths teacher... these questions require a 'bit' of =
Quadratic solution finding... ha, yeah right...

[ 2x^2 + x - 1 2x^2 - 5x + 3 ] [ 6x^2 + x - 2 ]
[ (2x - 1)(x + 1) (2x - 3) (x - 1) ] [(3x + 2)(2x - 1) ]
[ --------------- X ---------------- ] / [ --------------- ]
[ x^2 - 1 2x^2 - 7x + 3 ] [ 3x^2 - 7x - 6 ]
[ (x + 1)(x - 1) (2x - 1)(x - 3) ] [ (3x + 2)(x - 3) ]

There we are... the quadratics, now rip out the top line of each which =
is a demo working...
=20
[ (2x - 1)(x + 1) (2x - 3) (x - 1) ] [(3x + 2)(2x - 1) ]
[ --------------- X ---------------- ] / [ --------------- ]
[ (x + 1)(x - 1) (2x - 1)(x - 3) ] [ (3x + 2)(x - 3) ]

Now in the first 2nd level bracket, group the top and bottom row of =
terms together using standard multiplication of fraction methods.

[ (2x - 1)(x + 1)(2x - 3)(x - 1) ] [(3x + 2)(2x - 1) ]
[ ------------------------------- ] / [ --------------- ]
[ (x + 1)(x - 1)(2x - 1)(x - 3) ] [ (3x + 2)(x - 3) ]

Now cancel out the like terms in the numerator and denominator.

2x -1 is the first to go...

[ (CANCELED)(x + 1)(2x - 3)(x - 1) ] [(3x + 2)(2x - 1) ]
[ --------------------------------- ] / [ --------------- ]
[ (x + 1)(x - 1)(CANCELED)(x - 3) ] [ (3x + 2)(x - 3) ]

Second to be removed is (x + 1)...

[ (CANCELED)(2x - 3)(x - 1) ] [(3x + 2)(2x - 1) ]
[ -------------------------- ] / [ --------------- ]
[ (CANCELED)(x - 1)(x - 3) ] [ (3x + 2)(x - 3) ]

Then x - 1

[ (2x - 3)(CANCELED) ] [(3x + 2)(2x - 1) ]
[ ------------------ ] / [ --------------- ]
[ (CANCELED)(x - 3) ] [ (3x + 2)(x - 3) ]

Not forgeting the divisor, remove 3x + 2

[ (2x - 3) ] [ (CANCELED)(2x - 1) ]
[ -------- ] / [ ------------------ ]
[ (x - 3) ] [ (CANCELED)(x - 3) ]

Leaving us with....

[ (2x - 3) ] [(2x - 1) ]
[ -------- ] / [ ------- ]
[ (x - 3) ] [ (x - 3) ]

The we times and flip the division giving us...

[ (2x - 3) ] [ (x - 3) ]
[ -------- ] X [ ------- ]
[ (x - 3) ] [ 2x - 1) ]

x - 3 and x - 3 cancel out leaving us with.......

[ (2x - 3) ]
[ -------- ]
[ 2x - 1) ]

Which is, the correct answer >:) This took about half an hour to do the =
ruddy question to start with (and even longer to type it out in here! =
lol... question 2 of 5 done.. on to #3)

And THAT my friends, is why you should think twice about taking A2 pure =
mathmatics... (This is A2 P4)

- Mark
Gahhhhhh!!!
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charset="iso-8859-1"
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Diso-8859-1">
<META content=3D"MSHTML 6.00.2800.1226" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff><FONT face=3DArial><FONT size=3D2>
<DIV><FONT face=3D"Courier New">This is the very description of pain.. =
and its in=20
HTML because I require a fixed width font &gt;:)</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">Simplify:</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">[ 2x^2 + x - 1&nbsp;&nbsp;&nbsp;2x^2 - =
5x + 3=20
]&nbsp;&nbsp; [6x^2 + x - 2 ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ ------------ X ------------- ]&nbsp;/=20
[-------------]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;&nbsp; x^2 -=20
1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2x^2 - 7x + 3 ]&nbsp;&nbsp; [3x^2 - 7x - =

6]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">Now according to my maths teacher... =
these=20
questions require a 'bit' of Quadratic solution finding... ha, yeah=20
right...</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;&nbsp; 2x^2 + x - =
1&nbsp;&nbsp;&nbsp;&nbsp;=20
2x^2 - 5x + 3&nbsp;&nbsp; ]&nbsp;&nbsp; [&nbsp; 6x^2 + x - 2&nbsp;&nbsp; =

]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ (2x - 1)(x + 1)&nbsp;&nbsp; (2x - 3) =
(x - 1)=20
]&nbsp;&nbsp; [(3x + 2)(2x - 1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ =
---------------&nbsp;X&nbsp;----------------=20
]&nbsp;/ [ --------------- ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; x^2 -=20
1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2x^2 - 7x +=20
3&nbsp;&nbsp;]&nbsp;&nbsp; [&nbsp; 3x^2 - 7x - 6&nbsp; ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (x + 1)(x - 1)&nbsp;&nbsp;&nbsp; =
(2x -=20
1)(x - 3) ]&nbsp;&nbsp; [&nbsp;(3x + 2)(x - 3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">There we are... the quadratics, now rip =
out the=20
top line of each which is a demo working...</FONT></DIV></DIV>
<DIV><FONT face=3D"Courier New">&nbsp;</FONT>=20
<DIV><FONT face=3D"Courier New">[ (2x - 1)(x + 1)&nbsp;&nbsp; (2x - 3) =
(x - 1)=20
]&nbsp;&nbsp; [(3x + 2)(2x - 1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ =
---------------&nbsp;X&nbsp;----------------=20
]&nbsp;/ [ --------------- ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (x + 1)(x - 1)&nbsp;&nbsp;&nbsp; =
(2x -=20
1)(x - 3) ]&nbsp;&nbsp; [&nbsp;(3x + 2)(x - 3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">Now in the first 2nd level bracket, =
group the top=20
and bottom row of terms together using standard multiplication of =
fraction=20
methods.</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[ (2x - 1)(x + 1)(2x - 3)(x - 1)&nbsp;=20
]&nbsp;&nbsp; [(3x + 2)(2x - 1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ ------------------------------- =
]&nbsp;/ [=20
--------------- ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (x + 1)(x - 1)(2x - 1)(x - =
3)&nbsp;=20
]&nbsp;&nbsp; [&nbsp;(3x + 2)(x - 3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">Now cancel out the like terms in the =
numerator and=20
denominator.</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">2x -1 is the first to go...</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[ (CANCELED)(x + 1)(2x - 3)(x - 1)&nbsp; =

]&nbsp;&nbsp; [(3x + 2)(2x - 1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ =
---------------------------------&nbsp;]&nbsp;/=20
[ --------------- ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (x + 1)(x - 1)(CANCELED)(x - =
3)&nbsp;=20
]&nbsp;&nbsp; [&nbsp;(3x + 2)(x - 3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">Second to be removed is (x&nbsp;+=20
1)...</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[ (CANCELED)(2x - 3)(x - 1)&nbsp; =
]&nbsp;&nbsp;=20
[(3x + 2)(2x - 1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ =
--------------------------&nbsp;]&nbsp;/ [=20
--------------- ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (CANCELED)(x - 1)(x - 3)&nbsp;=20
]&nbsp;&nbsp; [&nbsp;(3x + 2)(x - 3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV>
<DIV><FONT face=3D"Courier New">Then x - 1</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;(2x - =
3)(CANCELED)&nbsp;]&nbsp;&nbsp; [(3x=20
+ 2)(2x - 1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ ------------------&nbsp;]&nbsp;/ [=20
--------------- ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (CANCELED)(x - =
3)&nbsp;]&nbsp;&nbsp;=20
[&nbsp;(3x + 2)(x - 3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV>
<DIV><FONT face=3D"Courier New">Not forgeting the divisor, remove 3x +=20
2</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;(2x - 3) ]&nbsp;&nbsp; [ =
(CANCELED)(2x - 1)=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ --------&nbsp;]&nbsp;/ [ =
------------------=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (x - 3)&nbsp;]&nbsp;&nbsp; =
[&nbsp;=20
(CANCELED)(x - 3)&nbsp;]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">Leaving us with....</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;(2x - 3) ]&nbsp;&nbsp; [(2x - 1)=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ --------&nbsp;]&nbsp;/ [ ------- =
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (x - 3)&nbsp;]&nbsp;&nbsp; =
[&nbsp;(x - 3)=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">The we times and flip the division =
giving=20
us...</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;(2x - 3) ]&nbsp;&nbsp; [ (x - 3)=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ --------&nbsp;]&nbsp;X [ ------- =
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (x - 3)&nbsp;]&nbsp;&nbsp; =
[&nbsp;2x - 1)=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">x - 3 and x - 3 cancel out leaving us=20
with.......</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;(2x - 3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ --------&nbsp;]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; 2x - 1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">Which is, the correct answer &gt;:) This =
took=20
about half an hour to&nbsp;do the ruddy question&nbsp; to start with =
(and even=20
longer to type it out in here! lol... question 2 of 5 done.. on to=20
#3)</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">And THAT my friends, is why you should =
think twice=20
about taking A2 pure mathmatics... (This is A2 P4)</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">- Mark</FONT></DIV>
<DIV><FONT=20
face=3D"Courier =
New">Gahhhhhh!!!</FONT></DIV></DIV></DIV></DIV></DIV></DIV></DIV></DIV></=
DIV></DIV></DIV></DIV></DIV></DIV></DIV></FONT></FONT></BODY></HTML>

------=_NextPart_000_0027_01C37225.9A531B40--

jerme

Sep 3, 2003, 4:54pm
A2 = Algebra II in the US?

That's not so bad... just wait until you find out what a derrivative is ;-)
Calculus is fun.

-Jeremy

P.S. Physics isn't real. Believe in magic.

--
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Jeremy Booker - Owner / Webmaster
JTech Web Systems
www.JTechWebSystems.com
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
"Therefore do not worry about tomorrow, for tomorrow will worry about
itself. Each day has enough trouble of its own." -Mathew 5:34




[View Quote] Simplify:

[ 2x^2 + x - 1 2x^2 - 5x + 3 ] [6x^2 + x - 2 ]
[ ------------ X ------------- ] / [-------------]
[ x^2 - 1 2x^2 - 7x + 3 ] [3x^2 - 7x - 6]

Now according to my maths teacher... these questions require a 'bit' of
Quadratic solution finding... ha, yeah right...

[ 2x^2 + x - 1 2x^2 - 5x + 3 ] [ 6x^2 + x - 2 ]
[ (2x - 1)(x + 1) (2x - 3) (x - 1) ] [(3x + 2)(2x - 1) ]
[ --------------- X ---------------- ] / [ --------------- ]
[ x^2 - 1 2x^2 - 7x + 3 ] [ 3x^2 - 7x - 6 ]
[ (x + 1)(x - 1) (2x - 1)(x - 3) ] [ (3x + 2)(x - 3) ]

There we are... the quadratics, now rip out the top line of each which is a
demo working...

[ (2x - 1)(x + 1) (2x - 3) (x - 1) ] [(3x + 2)(2x - 1) ]
[ --------------- X ---------------- ] / [ --------------- ]
[ (x + 1)(x - 1) (2x - 1)(x - 3) ] [ (3x + 2)(x - 3) ]

Now in the first 2nd level bracket, group the top and bottom row of terms
together using standard multiplication of fraction methods.

[ (2x - 1)(x + 1)(2x - 3)(x - 1) ] [(3x + 2)(2x - 1) ]
[ ------------------------------- ] / [ --------------- ]
[ (x + 1)(x - 1)(2x - 1)(x - 3) ] [ (3x + 2)(x - 3) ]

Now cancel out the like terms in the numerator and denominator.

2x -1 is the first to go...

[ (CANCELED)(x + 1)(2x - 3)(x - 1) ] [(3x + 2)(2x - 1) ]
[ --------------------------------- ] / [ --------------- ]
[ (x + 1)(x - 1)(CANCELED)(x - 3) ] [ (3x + 2)(x - 3) ]

Second to be removed is (x + 1)...

[ (CANCELED)(2x - 3)(x - 1) ] [(3x + 2)(2x - 1) ]
[ -------------------------- ] / [ --------------- ]
[ (CANCELED)(x - 1)(x - 3) ] [ (3x + 2)(x - 3) ]

Then x - 1

[ (2x - 3)(CANCELED) ] [(3x + 2)(2x - 1) ]
[ ------------------ ] / [ --------------- ]
[ (CANCELED)(x - 3) ] [ (3x + 2)(x - 3) ]

Not forgeting the divisor, remove 3x + 2

[ (2x - 3) ] [ (CANCELED)(2x - 1) ]
[ -------- ] / [ ------------------ ]
[ (x - 3) ] [ (CANCELED)(x - 3) ]

Leaving us with....

[ (2x - 3) ] [(2x - 1) ]
[ -------- ] / [ ------- ]
[ (x - 3) ] [ (x - 3) ]

The we times and flip the division giving us...

[ (2x - 3) ] [ (x - 3) ]
[ -------- ] X [ ------- ]
[ (x - 3) ] [ 2x - 1) ]

x - 3 and x - 3 cancel out leaving us with.......

[ (2x - 3) ]
[ -------- ]
[ 2x - 1) ]

Which is, the correct answer >:) This took about half an hour to do the
ruddy question to start with (and even longer to type it out in here!
lol... question 2 of 5 done.. on to #3)

And THAT my friends, is why you should think twice about taking A2 pure
mathmatics... (This is A2 P4)

- Mark
Gahhhhhh!!!

strike rapier

Sep 3, 2003, 5:02pm
Erm... A2 is the last year before uni...

And Calculus.. been there... Intergration, Differentiation, Rangefinding,
Mechanics, Derviving Logs, Deriving projectile formulae though squared
functions etc, blah blah blah.. Did it almost a year ago...

- Mark

[View Quote]

strike rapier

Sep 3, 2003, 5:06pm
I presume you mean:

(A*N)x^(n-1)

and

(A/N+1)x^(N+1)

:)

- Mark

[View Quote]

bowen

Sep 3, 2003, 6:50pm
[View Quote] Uh no, that's what you learn in algebra about derivation. Wait until
you get into conical proofs of derivatives, oh not just that, inverse
area proof for derivation and things so peachy and fun as that.

--
--Bowen--
http://bowen.homelinux.com/sys/
Yeah, it's that good.
(Maybe an AW section in the near future?)

strike rapier

Sep 3, 2003, 6:59pm
Erm... the algebra form of doing it... Do you think I'm going to write out
the entire 12 or so chapters of work on it? Thats like 6 months worth...

- Mark

[View Quote]

bowen

Sep 3, 2003, 8:31pm
[View Quote] Which is why algebra is different from calculus. Even then, it's more
than 6 months of work, because the forumlas for what I stated are not in
that form, but use limits and things like those. Yeah, it's mighty
different, just ask jerme, he knows.

--
--Bowen--
http://bowen.homelinux.com/sys/
Yeah, it's that good.
(Maybe an AW section in the near future?)

.duo.

Sep 3, 2003, 10:38pm
This is a multi-part message in MIME format.

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I can finish my school's entire math curriculum in less than a year. I =
just haven't yet, lol.

--=20
-.Duo. (342836)
[View Quote] Simplify:

[ 2x^2 + x - 1 2x^2 - 5x + 3 ] [6x^2 + x - 2 ]
[ ------------ X ------------- ] / [-------------]
[ x^2 - 1 2x^2 - 7x + 3 ] [3x^2 - 7x - 6]

Now according to my maths teacher... these questions require a 'bit' =
of Quadratic solution finding... ha, yeah right...

[ 2x^2 + x - 1 2x^2 - 5x + 3 ] [ 6x^2 + x - 2 ]
[ (2x - 1)(x + 1) (2x - 3) (x - 1) ] [(3x + 2)(2x - 1) ]
[ --------------- X ---------------- ] / [ --------------- ]
[ x^2 - 1 2x^2 - 7x + 3 ] [ 3x^2 - 7x - 6 ]
[ (x + 1)(x - 1) (2x - 1)(x - 3) ] [ (3x + 2)(x - 3) ]

There we are... the quadratics, now rip out the top line of each which =
is a demo working...
=20
[ (2x - 1)(x + 1) (2x - 3) (x - 1) ] [(3x + 2)(2x - 1) ]
[ --------------- X ---------------- ] / [ --------------- ]
[ (x + 1)(x - 1) (2x - 1)(x - 3) ] [ (3x + 2)(x - 3) ]

Now in the first 2nd level bracket, group the top and bottom row of =
terms together using standard multiplication of fraction methods.

[ (2x - 1)(x + 1)(2x - 3)(x - 1) ] [(3x + 2)(2x - 1) ]
[ ------------------------------- ] / [ --------------- ]
[ (x + 1)(x - 1)(2x - 1)(x - 3) ] [ (3x + 2)(x - 3) ]

Now cancel out the like terms in the numerator and denominator.

2x -1 is the first to go...

[ (CANCELED)(x + 1)(2x - 3)(x - 1) ] [(3x + 2)(2x - 1) ]
[ --------------------------------- ] / [ --------------- ]
[ (x + 1)(x - 1)(CANCELED)(x - 3) ] [ (3x + 2)(x - 3) ]

Second to be removed is (x + 1)...

[ (CANCELED)(2x - 3)(x - 1) ] [(3x + 2)(2x - 1) ]
[ -------------------------- ] / [ --------------- ]
[ (CANCELED)(x - 1)(x - 3) ] [ (3x + 2)(x - 3) ]

Then x - 1

[ (2x - 3)(CANCELED) ] [(3x + 2)(2x - 1) ]
[ ------------------ ] / [ --------------- ]
[ (CANCELED)(x - 3) ] [ (3x + 2)(x - 3) ]

Not forgeting the divisor, remove 3x + 2

[ (2x - 3) ] [ (CANCELED)(2x - 1) ]
[ -------- ] / [ ------------------ ]
[ (x - 3) ] [ (CANCELED)(x - 3) ]

Leaving us with....

[ (2x - 3) ] [(2x - 1) ]
[ -------- ] / [ ------- ]
[ (x - 3) ] [ (x - 3) ]

The we times and flip the division giving us...

[ (2x - 3) ] [ (x - 3) ]
[ -------- ] X [ ------- ]
[ (x - 3) ] [ 2x - 1) ]

x - 3 and x - 3 cancel out leaving us with.......

[ (2x - 3) ]
[ -------- ]
[ 2x - 1) ]

Which is, the correct answer >:) This took about half an hour to do =
the ruddy question to start with (and even longer to type it out in =
here! lol... question 2 of 5 done.. on to #3)

And THAT my friends, is why you should think twice about taking A2 =
pure mathmatics... (This is A2 P4)

- Mark
Gahhhhhh!!!
------=_NextPart_000_0068_01C3725A.352F47E0
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charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Diso-8859-1">
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<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT face=3DArial size=3D2>I can finish my school's entire math =
curriculum in=20
less than a year. I just haven't yet, lol.</FONT></DIV>
<DIV><BR>-- <BR>-.Duo. (342836)</DIV>
<BLOCKQUOTE dir=3Dltr=20
style=3D"PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; =
BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV>"strike rapier" &lt;<A=20
=
href=3D"mailto:strike at Rapiercom.freeserve.co.uk">strike at Rapiercom.freeser=
ve.co.uk</A>&gt;=20
[View Quote] ]&nbsp;&nbsp; [(3x + 2)(2x - 1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ ------------------------------- =
]&nbsp;/ [=20
--------------- ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (x + 1)(x - 1)(2x - 1)(x - =
3)&nbsp;=20
]&nbsp;&nbsp; [&nbsp;(3x + 2)(x - 3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">Now cancel out the like terms in the =
numerator=20
and denominator.</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">2x -1 is the first to =
go...</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[ (CANCELED)(x + 1)(2x - 3)(x - =
1)&nbsp;=20
]&nbsp;&nbsp; [(3x + 2)(2x - 1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[=20
---------------------------------&nbsp;]&nbsp;/ [ ---------------=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (x + 1)(x - 1)(CANCELED)(x - =
3)&nbsp;=20
]&nbsp;&nbsp; [&nbsp;(3x + 2)(x - 3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">Second to be removed is (x&nbsp;+=20
1)...</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[ (CANCELED)(2x - 3)(x - 1)&nbsp; =
]&nbsp;&nbsp;=20
[(3x + 2)(2x - 1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ =
--------------------------&nbsp;]&nbsp;/ [=20
--------------- ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (CANCELED)(x - 1)(x - 3)&nbsp; =

]&nbsp;&nbsp; [&nbsp;(3x + 2)(x - 3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV>
<DIV><FONT face=3D"Courier New">Then x - 1</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;(2x - =
3)(CANCELED)&nbsp;]&nbsp;&nbsp;=20
[(3x + 2)(2x - 1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ ------------------&nbsp;]&nbsp;/ [=20
--------------- ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (CANCELED)(x - =
3)&nbsp;]&nbsp;&nbsp;=20
[&nbsp;(3x + 2)(x - 3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV>
<DIV><FONT face=3D"Courier New">Not forgeting the divisor, remove 3x + =

2</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;(2x - 3) ]&nbsp;&nbsp; [ =
(CANCELED)(2x -=20
1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ --------&nbsp;]&nbsp;/ [ =
------------------=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (x - 3)&nbsp;]&nbsp;&nbsp; =
[&nbsp;=20
(CANCELED)(x - 3)&nbsp;]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">Leaving us with....</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;(2x - 3) ]&nbsp;&nbsp; [(2x - =
1)=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ --------&nbsp;]&nbsp;/ [ -------=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (x - 3)&nbsp;]&nbsp;&nbsp; =
[&nbsp;(x -=20
3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">The we times and flip the division =
giving=20
us...</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;(2x - 3) ]&nbsp;&nbsp; [ (x - =
3)=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ --------&nbsp;]&nbsp;X [ -------=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (x - 3)&nbsp;]&nbsp;&nbsp; =
[&nbsp;2x -=20
1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">x - 3 and x - 3 cancel out leaving us=20
with.......</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;(2x - 3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ --------&nbsp;]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; 2x - 1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">Which is, the correct answer &gt;:) =
This took=20
about half an hour to&nbsp;do the ruddy question&nbsp; to start with =
(and even=20
longer to type it out in here! lol... question 2 of 5 done.. on to=20
#3)</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">And THAT my friends, is why you should =
think=20
twice about taking A2 pure mathmatics... (This is A2 P4)</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">- Mark</FONT></DIV>
<DIV><FONT=20
face=3D"Courier =
New">Gahhhhhh!!!</FONT></DIV></DIV></DIV></DIV></DIV></DIV></DIV></DIV></=
DIV></DIV></DIV></DIV></DIV></DIV></DIV></BLOCKQUOTE></FONT></FONT></BODY=
></HTML>

------=_NextPart_000_0068_01C3725A.352F47E0--

.duo.

Sep 3, 2003, 10:40pm
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That's algebra 2? I haven't even taken that and I know how to solve =
that...

--=20
-.Duo. (342836)
[View Quote] Simplify:

[ 2x^2 + x - 1 2x^2 - 5x + 3 ] [6x^2 + x - 2 ]
[ ------------ X ------------- ] / [-------------]
[ x^2 - 1 2x^2 - 7x + 3 ] [3x^2 - 7x - 6]

Now according to my maths teacher... these questions require a 'bit' =
of Quadratic solution finding... ha, yeah right...

[ 2x^2 + x - 1 2x^2 - 5x + 3 ] [ 6x^2 + x - 2 ]
[ (2x - 1)(x + 1) (2x - 3) (x - 1) ] [(3x + 2)(2x - 1) ]
[ --------------- X ---------------- ] / [ --------------- ]
[ x^2 - 1 2x^2 - 7x + 3 ] [ 3x^2 - 7x - 6 ]
[ (x + 1)(x - 1) (2x - 1)(x - 3) ] [ (3x + 2)(x - 3) ]

There we are... the quadratics, now rip out the top line of each which =
is a demo working...
=20
[ (2x - 1)(x + 1) (2x - 3) (x - 1) ] [(3x + 2)(2x - 1) ]
[ --------------- X ---------------- ] / [ --------------- ]
[ (x + 1)(x - 1) (2x - 1)(x - 3) ] [ (3x + 2)(x - 3) ]

Now in the first 2nd level bracket, group the top and bottom row of =
terms together using standard multiplication of fraction methods.

[ (2x - 1)(x + 1)(2x - 3)(x - 1) ] [(3x + 2)(2x - 1) ]
[ ------------------------------- ] / [ --------------- ]
[ (x + 1)(x - 1)(2x - 1)(x - 3) ] [ (3x + 2)(x - 3) ]

Now cancel out the like terms in the numerator and denominator.

2x -1 is the first to go...

[ (CANCELED)(x + 1)(2x - 3)(x - 1) ] [(3x + 2)(2x - 1) ]
[ --------------------------------- ] / [ --------------- ]
[ (x + 1)(x - 1)(CANCELED)(x - 3) ] [ (3x + 2)(x - 3) ]

Second to be removed is (x + 1)...

[ (CANCELED)(2x - 3)(x - 1) ] [(3x + 2)(2x - 1) ]
[ -------------------------- ] / [ --------------- ]
[ (CANCELED)(x - 1)(x - 3) ] [ (3x + 2)(x - 3) ]

Then x - 1

[ (2x - 3)(CANCELED) ] [(3x + 2)(2x - 1) ]
[ ------------------ ] / [ --------------- ]
[ (CANCELED)(x - 3) ] [ (3x + 2)(x - 3) ]

Not forgeting the divisor, remove 3x + 2

[ (2x - 3) ] [ (CANCELED)(2x - 1) ]
[ -------- ] / [ ------------------ ]
[ (x - 3) ] [ (CANCELED)(x - 3) ]

Leaving us with....

[ (2x - 3) ] [(2x - 1) ]
[ -------- ] / [ ------- ]
[ (x - 3) ] [ (x - 3) ]

The we times and flip the division giving us...

[ (2x - 3) ] [ (x - 3) ]
[ -------- ] X [ ------- ]
[ (x - 3) ] [ 2x - 1) ]

x - 3 and x - 3 cancel out leaving us with.......

[ (2x - 3) ]
[ -------- ]
[ 2x - 1) ]

Which is, the correct answer >:) This took about half an hour to do =
the ruddy question to start with (and even longer to type it out in =
here! lol... question 2 of 5 done.. on to #3)

And THAT my friends, is why you should think twice about taking A2 =
pure mathmatics... (This is A2 P4)

- Mark
Gahhhhhh!!!
------=_NextPart_000_0084_01C3725A.614598C0
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charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Diso-8859-1">
<META content=3D"MSHTML 6.00.2800.1226" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT face=3DArial size=3D2>That's algebra 2? I haven't even taken =
that and I=20
know how to solve that...</FONT></DIV>
<DIV><BR>-- <BR>-.Duo. (342836)</DIV>
<BLOCKQUOTE dir=3Dltr=20
style=3D"PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; =
BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV>"strike rapier" &lt;<A=20
=
href=3D"mailto:strike at Rapiercom.freeserve.co.uk">strike at Rapiercom.freeser=
ve.co.uk</A>&gt;=20
[View Quote] ]&nbsp;&nbsp; [(3x + 2)(2x - 1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ ------------------------------- =
]&nbsp;/ [=20
--------------- ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (x + 1)(x - 1)(2x - 1)(x - =
3)&nbsp;=20
]&nbsp;&nbsp; [&nbsp;(3x + 2)(x - 3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">Now cancel out the like terms in the =
numerator=20
and denominator.</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">2x -1 is the first to =
go...</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[ (CANCELED)(x + 1)(2x - 3)(x - =
1)&nbsp;=20
]&nbsp;&nbsp; [(3x + 2)(2x - 1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[=20
---------------------------------&nbsp;]&nbsp;/ [ ---------------=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (x + 1)(x - 1)(CANCELED)(x - =
3)&nbsp;=20
]&nbsp;&nbsp; [&nbsp;(3x + 2)(x - 3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">Second to be removed is (x&nbsp;+=20
1)...</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[ (CANCELED)(2x - 3)(x - 1)&nbsp; =
]&nbsp;&nbsp;=20
[(3x + 2)(2x - 1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ =
--------------------------&nbsp;]&nbsp;/ [=20
--------------- ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (CANCELED)(x - 1)(x - 3)&nbsp; =

]&nbsp;&nbsp; [&nbsp;(3x + 2)(x - 3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV>
<DIV><FONT face=3D"Courier New">Then x - 1</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;(2x - =
3)(CANCELED)&nbsp;]&nbsp;&nbsp;=20
[(3x + 2)(2x - 1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ ------------------&nbsp;]&nbsp;/ [=20
--------------- ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (CANCELED)(x - =
3)&nbsp;]&nbsp;&nbsp;=20
[&nbsp;(3x + 2)(x - 3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV>
<DIV><FONT face=3D"Courier New">Not forgeting the divisor, remove 3x + =

2</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;(2x - 3) ]&nbsp;&nbsp; [ =
(CANCELED)(2x -=20
1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ --------&nbsp;]&nbsp;/ [ =
------------------=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (x - 3)&nbsp;]&nbsp;&nbsp; =
[&nbsp;=20
(CANCELED)(x - 3)&nbsp;]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">Leaving us with....</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;(2x - 3) ]&nbsp;&nbsp; [(2x - =
1)=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ --------&nbsp;]&nbsp;/ [ -------=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (x - 3)&nbsp;]&nbsp;&nbsp; =
[&nbsp;(x -=20
3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">The we times and flip the division =
giving=20
us...</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;(2x - 3) ]&nbsp;&nbsp; [ (x - =
3)=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ --------&nbsp;]&nbsp;X [ -------=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (x - 3)&nbsp;]&nbsp;&nbsp; =
[&nbsp;2x -=20
1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">x - 3 and x - 3 cancel out leaving us=20
with.......</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;(2x - 3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ --------&nbsp;]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; 2x - 1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">Which is, the correct answer &gt;:) =
This took=20
about half an hour to&nbsp;do the ruddy question&nbsp; to start with =
(and even=20
longer to type it out in here! lol... question 2 of 5 done.. on to=20
#3)</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">And THAT my friends, is why you should =
think=20
twice about taking A2 pure mathmatics... (This is A2 P4)</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">- Mark</FONT></DIV>
<DIV><FONT=20
face=3D"Courier =
New">Gahhhhhh!!!</FONT></DIV></DIV></DIV></DIV></DIV></DIV></DIV></DIV></=
DIV></DIV></DIV></DIV></DIV></DIV></DIV></BLOCKQUOTE></FONT></FONT></BODY=
></HTML>

------=_NextPart_000_0084_01C3725A.614598C0--

mod

Sep 3, 2003, 10:45pm
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------=_NextPart_000_004A_01C3725A.DCCB25F0
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Content-Transfer-Encoding: quoted-printable

One word... Matrices *shivers*

-Mod


[View Quote] Simplify:

[ 2x^2 + x - 1 2x^2 - 5x + 3 ] [6x^2 + x - 2 ]
[ ------------ X ------------- ] / [-------------]
[ x^2 - 1 2x^2 - 7x + 3 ] [3x^2 - 7x - 6]

Now according to my maths teacher... these questions require a 'bit' =
of Quadratic solution finding... ha, yeah right...

[ 2x^2 + x - 1 2x^2 - 5x + 3 ] [ 6x^2 + x - 2 ]
[ (2x - 1)(x + 1) (2x - 3) (x - 1) ] [(3x + 2)(2x - 1) ]
[ --------------- X ---------------- ] / [ --------------- ]
[ x^2 - 1 2x^2 - 7x + 3 ] [ 3x^2 - 7x - 6 ]
[ (x + 1)(x - 1) (2x - 1)(x - 3) ] [ (3x + 2)(x - 3) ]

There we are... the quadratics, now rip out the top line of each which =
is a demo working...
=20
[ (2x - 1)(x + 1) (2x - 3) (x - 1) ] [(3x + 2)(2x - 1) ]
[ --------------- X ---------------- ] / [ --------------- ]
[ (x + 1)(x - 1) (2x - 1)(x - 3) ] [ (3x + 2)(x - 3) ]

Now in the first 2nd level bracket, group the top and bottom row of =
terms together using standard multiplication of fraction methods.

[ (2x - 1)(x + 1)(2x - 3)(x - 1) ] [(3x + 2)(2x - 1) ]
[ ------------------------------- ] / [ --------------- ]
[ (x + 1)(x - 1)(2x - 1)(x - 3) ] [ (3x + 2)(x - 3) ]

Now cancel out the like terms in the numerator and denominator.

2x -1 is the first to go...

[ (CANCELED)(x + 1)(2x - 3)(x - 1) ] [(3x + 2)(2x - 1) ]
[ --------------------------------- ] / [ --------------- ]
[ (x + 1)(x - 1)(CANCELED)(x - 3) ] [ (3x + 2)(x - 3) ]

Second to be removed is (x + 1)...

[ (CANCELED)(2x - 3)(x - 1) ] [(3x + 2)(2x - 1) ]
[ -------------------------- ] / [ --------------- ]
[ (CANCELED)(x - 1)(x - 3) ] [ (3x + 2)(x - 3) ]

Then x - 1

[ (2x - 3)(CANCELED) ] [(3x + 2)(2x - 1) ]
[ ------------------ ] / [ --------------- ]
[ (CANCELED)(x - 3) ] [ (3x + 2)(x - 3) ]

Not forgeting the divisor, remove 3x + 2

[ (2x - 3) ] [ (CANCELED)(2x - 1) ]
[ -------- ] / [ ------------------ ]
[ (x - 3) ] [ (CANCELED)(x - 3) ]

Leaving us with....

[ (2x - 3) ] [(2x - 1) ]
[ -------- ] / [ ------- ]
[ (x - 3) ] [ (x - 3) ]

The we times and flip the division giving us...

[ (2x - 3) ] [ (x - 3) ]
[ -------- ] X [ ------- ]
[ (x - 3) ] [ 2x - 1) ]

x - 3 and x - 3 cancel out leaving us with.......

[ (2x - 3) ]
[ -------- ]
[ 2x - 1) ]

Which is, the correct answer >:) This took about half an hour to do =
the ruddy question to start with (and even longer to type it out in =
here! lol... question 2 of 5 done.. on to #3)

And THAT my friends, is why you should think twice about taking A2 =
pure mathmatics... (This is A2 P4)

- Mark
Gahhhhhh!!!
------=_NextPart_000_004A_01C3725A.DCCB25F0
Content-Type: text/html;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Diso-8859-1">
<META content=3D"MSHTML 6.00.2800.1226" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT face=3DArial size=3D2>One word... Matrices =
*shivers*</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>-Mod</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV>&nbsp;</DIV>
<BLOCKQUOTE dir=3Dltr=20
style=3D"PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; =
BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV>"strike rapier" &lt;<A=20
=
href=3D"mailto:strike at Rapiercom.freeserve.co.uk">strike at Rapiercom.freeser=
ve.co.uk</A>&gt;=20
[View Quote] ]&nbsp;&nbsp; [(3x + 2)(2x - 1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ ------------------------------- =
]&nbsp;/ [=20
--------------- ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (x + 1)(x - 1)(2x - 1)(x - =
3)&nbsp;=20
]&nbsp;&nbsp; [&nbsp;(3x + 2)(x - 3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">Now cancel out the like terms in the =
numerator=20
and denominator.</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">2x -1 is the first to =
go...</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[ (CANCELED)(x + 1)(2x - 3)(x - =
1)&nbsp;=20
]&nbsp;&nbsp; [(3x + 2)(2x - 1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[=20
---------------------------------&nbsp;]&nbsp;/ [ ---------------=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (x + 1)(x - 1)(CANCELED)(x - =
3)&nbsp;=20
]&nbsp;&nbsp; [&nbsp;(3x + 2)(x - 3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">Second to be removed is (x&nbsp;+=20
1)...</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[ (CANCELED)(2x - 3)(x - 1)&nbsp; =
]&nbsp;&nbsp;=20
[(3x + 2)(2x - 1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ =
--------------------------&nbsp;]&nbsp;/ [=20
--------------- ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (CANCELED)(x - 1)(x - 3)&nbsp; =

]&nbsp;&nbsp; [&nbsp;(3x + 2)(x - 3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV>
<DIV><FONT face=3D"Courier New">Then x - 1</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;(2x - =
3)(CANCELED)&nbsp;]&nbsp;&nbsp;=20
[(3x + 2)(2x - 1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ ------------------&nbsp;]&nbsp;/ [=20
--------------- ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (CANCELED)(x - =
3)&nbsp;]&nbsp;&nbsp;=20
[&nbsp;(3x + 2)(x - 3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV>
<DIV><FONT face=3D"Courier New">Not forgeting the divisor, remove 3x + =

2</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;(2x - 3) ]&nbsp;&nbsp; [ =
(CANCELED)(2x -=20
1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ --------&nbsp;]&nbsp;/ [ =
------------------=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (x - 3)&nbsp;]&nbsp;&nbsp; =
[&nbsp;=20
(CANCELED)(x - 3)&nbsp;]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">Leaving us with....</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;(2x - 3) ]&nbsp;&nbsp; [(2x - =
1)=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ --------&nbsp;]&nbsp;/ [ -------=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (x - 3)&nbsp;]&nbsp;&nbsp; =
[&nbsp;(x -=20
3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">The we times and flip the division =
giving=20
us...</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;(2x - 3) ]&nbsp;&nbsp; [ (x - =
3)=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ --------&nbsp;]&nbsp;X [ -------=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (x - 3)&nbsp;]&nbsp;&nbsp; =
[&nbsp;2x -=20
1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">x - 3 and x - 3 cancel out leaving us=20
with.......</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;(2x - 3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ --------&nbsp;]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; 2x - 1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">Which is, the correct answer &gt;:) =
This took=20
about half an hour to&nbsp;do the ruddy question&nbsp; to start with =
(and even=20
longer to type it out in here! lol... question 2 of 5 done.. on to=20
#3)</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">And THAT my friends, is why you should =
think=20
twice about taking A2 pure mathmatics... (This is A2 P4)</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">- Mark</FONT></DIV>
<DIV><FONT=20
face=3D"Courier =
New">Gahhhhhh!!!</FONT></DIV></DIV></DIV></DIV></DIV></DIV></DIV></DIV></=
DIV></DIV></DIV></DIV></DIV></DIV></DIV></BLOCKQUOTE></FONT></FONT></BODY=
></HTML>

------=_NextPart_000_004A_01C3725A.DCCB25F0--

bowen

Sep 4, 2003, 12:11am
[View Quote] All he's doing is simplifying a quadratic equation's operations. It's
really simple and takes about 2 minutes if you know what you're doing.

--
--Bowen--
http://bowen.homelinux.com/sys/
Yeah, it's that good.
(Maybe an AW section in the near future?)

bowen

Sep 4, 2003, 5:38am
[View Quote] Buy a calculator. It'll be the best $100 you ever spent and you learn
how to program _REAL_ basic.

--
--Bowen--
http://bowen.homelinux.com/sys/
Yeah, it's that good.
(Maybe an AW section in the near future?)

king small guy

Sep 4, 2003, 4:36pm
This is a multi-part message in MIME format.

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Its a question with no answer.
--=20

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D
King small guy #350914

http://ksg.250free.com
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D
[View Quote] Simplify:

[ 2x^2 + x - 1 2x^2 - 5x + 3 ] [6x^2 + x - 2 ]
[ ------------ X ------------- ] / [-------------]
[ x^2 - 1 2x^2 - 7x + 3 ] [3x^2 - 7x - 6]

Now according to my maths teacher... these questions require a 'bit' =
of Quadratic solution finding... ha, yeah right...

[ 2x^2 + x - 1 2x^2 - 5x + 3 ] [ 6x^2 + x - 2 ]
[ (2x - 1)(x + 1) (2x - 3) (x - 1) ] [(3x + 2)(2x - 1) ]
[ --------------- X ---------------- ] / [ --------------- ]
[ x^2 - 1 2x^2 - 7x + 3 ] [ 3x^2 - 7x - 6 ]
[ (x + 1)(x - 1) (2x - 1)(x - 3) ] [ (3x + 2)(x - 3) ]

There we are... the quadratics, now rip out the top line of each which =
is a demo working...
=20
[ (2x - 1)(x + 1) (2x - 3) (x - 1) ] [(3x + 2)(2x - 1) ]
[ --------------- X ---------------- ] / [ --------------- ]
[ (x + 1)(x - 1) (2x - 1)(x - 3) ] [ (3x + 2)(x - 3) ]

Now in the first 2nd level bracket, group the top and bottom row of =
terms together using standard multiplication of fraction methods.

[ (2x - 1)(x + 1)(2x - 3)(x - 1) ] [(3x + 2)(2x - 1) ]
[ ------------------------------- ] / [ --------------- ]
[ (x + 1)(x - 1)(2x - 1)(x - 3) ] [ (3x + 2)(x - 3) ]

Now cancel out the like terms in the numerator and denominator.

2x -1 is the first to go...

[ (CANCELED)(x + 1)(2x - 3)(x - 1) ] [(3x + 2)(2x - 1) ]
[ --------------------------------- ] / [ --------------- ]
[ (x + 1)(x - 1)(CANCELED)(x - 3) ] [ (3x + 2)(x - 3) ]

Second to be removed is (x + 1)...

[ (CANCELED)(2x - 3)(x - 1) ] [(3x + 2)(2x - 1) ]
[ -------------------------- ] / [ --------------- ]
[ (CANCELED)(x - 1)(x - 3) ] [ (3x + 2)(x - 3) ]

Then x - 1

[ (2x - 3)(CANCELED) ] [(3x + 2)(2x - 1) ]
[ ------------------ ] / [ --------------- ]
[ (CANCELED)(x - 3) ] [ (3x + 2)(x - 3) ]

Not forgeting the divisor, remove 3x + 2

[ (2x - 3) ] [ (CANCELED)(2x - 1) ]
[ -------- ] / [ ------------------ ]
[ (x - 3) ] [ (CANCELED)(x - 3) ]

Leaving us with....

[ (2x - 3) ] [(2x - 1) ]
[ -------- ] / [ ------- ]
[ (x - 3) ] [ (x - 3) ]

The we times and flip the division giving us...

[ (2x - 3) ] [ (x - 3) ]
[ -------- ] X [ ------- ]
[ (x - 3) ] [ 2x - 1) ]

x - 3 and x - 3 cancel out leaving us with.......

[ (2x - 3) ]
[ -------- ]
[ 2x - 1) ]

Which is, the correct answer >:) This took about half an hour to do =
the ruddy question to start with (and even longer to type it out in =
here! lol... question 2 of 5 done.. on to #3)

And THAT my friends, is why you should think twice about taking A2 =
pure mathmatics... (This is A2 P4)

- Mark
Gahhhhhh!!!

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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Diso-8859-1">
<META content=3D"MSHTML 5.50.4134.100" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT face=3DArial size=3D2>Its a question with no answer.<BR>-- =
</FONT></DIV>
<DIV>&nbsp;</DIV>
<DIV><FONT face=3DArial =
size=3D2>=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D<BR>King small guy=20
#350914</FONT></DIV>
<DIV>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2><A=20
href=3D"http://ksg.250free.com">http://ksg.250free.com</A><BR>=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D</FONT></DIV>
<BLOCKQUOTE dir=3Dltr=20
style=3D"PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; =
BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV>"strike rapier" &lt;<A=20
=
href=3D"mailto:strike at Rapiercom.freeserve.co.uk">strike at Rapiercom.freeser=
ve.co.uk</A>&gt;=20
[View Quote] ]&nbsp;&nbsp; [(3x + 2)(2x - 1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ ------------------------------- =
]&nbsp;/ [=20
--------------- ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (x + 1)(x - 1)(2x - 1)(x - =
3)&nbsp;=20
]&nbsp;&nbsp; [&nbsp;(3x + 2)(x - 3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">Now cancel out the like terms in the =
numerator=20
and denominator.</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">2x -1 is the first to =
go...</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[ (CANCELED)(x + 1)(2x - 3)(x - =
1)&nbsp;=20
]&nbsp;&nbsp; [(3x + 2)(2x - 1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[=20
---------------------------------&nbsp;]&nbsp;/ [ ---------------=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (x + 1)(x - 1)(CANCELED)(x - =
3)&nbsp;=20
]&nbsp;&nbsp; [&nbsp;(3x + 2)(x - 3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">Second to be removed is (x&nbsp;+=20
1)...</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[ (CANCELED)(2x - 3)(x - 1)&nbsp; =
]&nbsp;&nbsp;=20
[(3x + 2)(2x - 1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ =
--------------------------&nbsp;]&nbsp;/ [=20
--------------- ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (CANCELED)(x - 1)(x - 3)&nbsp; =

]&nbsp;&nbsp; [&nbsp;(3x + 2)(x - 3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV>
<DIV><FONT face=3D"Courier New">Then x - 1</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;(2x - =
3)(CANCELED)&nbsp;]&nbsp;&nbsp;=20
[(3x + 2)(2x - 1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ ------------------&nbsp;]&nbsp;/ [=20
--------------- ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (CANCELED)(x - =
3)&nbsp;]&nbsp;&nbsp;=20
[&nbsp;(3x + 2)(x - 3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV>
<DIV><FONT face=3D"Courier New">Not forgeting the divisor, remove 3x + =

2</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;(2x - 3) ]&nbsp;&nbsp; [ =
(CANCELED)(2x -=20
1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ --------&nbsp;]&nbsp;/ [ =
------------------=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (x - 3)&nbsp;]&nbsp;&nbsp; =
[&nbsp;=20
(CANCELED)(x - 3)&nbsp;]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">Leaving us with....</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;(2x - 3) ]&nbsp;&nbsp; [(2x - =
1)=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ --------&nbsp;]&nbsp;/ [ -------=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (x - 3)&nbsp;]&nbsp;&nbsp; =
[&nbsp;(x -=20
3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">The we times and flip the division =
giving=20
us...</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;(2x - 3) ]&nbsp;&nbsp; [ (x - =
3)=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ --------&nbsp;]&nbsp;X [ -------=20
]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; (x - 3)&nbsp;]&nbsp;&nbsp; =
[&nbsp;2x -=20
1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">x - 3 and x - 3 cancel out leaving us=20
with.......</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV>
<DIV><FONT face=3D"Courier New">[&nbsp;(2x - 3) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[ --------&nbsp;]</FONT></DIV>
<DIV><FONT face=3D"Courier New">[&nbsp; 2x - 1) ]</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">Which is, the correct answer &gt;:) =
This took=20
about half an hour to&nbsp;do the ruddy question&nbsp; to start with =
(and even=20
longer to type it out in here! lol... question 2 of 5 done.. on to=20
#3)</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">And THAT my friends, is why you should =
think=20
twice about taking A2 pure mathmatics... (This is A2 P4)</FONT></DIV>
<DIV><FONT face=3D"Courier New"></FONT>&nbsp;</DIV>
<DIV><FONT face=3D"Courier New">- Mark</FONT></DIV>
<DIV><FONT=20
face=3D"Courier =
New">Gahhhhhh!!!</FONT></DIV></DIV></DIV></DIV></DIV></DIV></DIV></DIV></=
DIV></DIV></DIV></DIV></DIV></DIV></DIV></BLOCKQUOTE></FONT></FONT></BODY=
></HTML>

------=_NextPart_000_006D_01C3731A.9C019840--

.duo.

Sep 4, 2003, 7:56pm
lol, guess so. BTW, I'm not clipping my posts just to torture strike >:-P

--
-.Duo. (342836)
[View Quote]

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