# Simplify ......

• Aug 22nd 2011, 06:59 PM
StudentMCCS
Simplify ......
Simplify

[(-16x^2+29x+6)-(16t^2+29t+6)]/x-t

I noticed I can factor into (-x+2)(16x+3) etc..

But, they are asking me to simplify. As far as I know, all this means is that I can simplify the top and get, [-16x^2+29x+16t^2-29t]/x-t. Do you think this is what they want? Or am I missing something?
• Aug 22nd 2011, 07:05 PM
Prove It
Re: Simplify ......
Quote:

Originally Posted by StudentMCCS
Simplify

[(-16x^2+29x+6)-(16t^2+29t+6)]/x-t

I noticed I can factor into (-x+2)(16x+3) etc..

But, they are asking me to simplify. As far as I know, all this means is that I can simplify the top and get, [-16x^2+29x+16t^2-29t]/x-t. Do you think this is what they want? Or am I missing something?

OK first of all, I doubt you could have written the question correctly. Should the second lot of brackets start with -16t^2?
• Aug 22nd 2011, 07:13 PM
Quacky
Re: Simplify ......
Quote:

Originally Posted by StudentMCCS
Simplify

[(-16x^2+29x+6)-(16t^2+29t+6)]/x-t

I noticed I can factor into (-x+2)(16x+3) etc..

But, they are asking me to simplify. As far as I know, all this means is that I can simplify the top and get, [-16x^2+29x+16t^2-29t]/x-t. Do you think this is what they want? Or am I missing something?

Hey, great start. You're almost there. Once you're at this stage:

$\displaystyle \frac{(-16x^2+29x+16t^2-29t)}{x-t}$

Rewrite:

$\displaystyle \frac{(16t^2-16x^2+29x-29t)}{x-t}$

Partially factor:

$\displaystyle \frac{(16(t+x)(t-x))+29(x-t))}{x-t}$

Rewrite, changing the signs of the $\displaystyle 16$ and then second bracket (changing the $\displaystyle 16$ to $\displaystyle -16$ is the same as multiplying through by $\displaystyle -1$, changing the signs of the second bracket multiplies through by $\displaystyle -1$ again, so the end result is unchanged):

$\displaystyle \frac{(-16(t+x)(-t+x))+29(x-t))}{x-t}$

Rewrite again, just for clarity:

$\displaystyle \frac{(-16(t+x)(x-t))+29(x-t))}{x-t}$

And then we can cancel:

$\displaystyle -16(t+x)+29$ (remembering that $\displaystyle x\neq t$)
• Aug 22nd 2011, 07:13 PM
StudentMCCS
Re: Simplify ......
Quote:

Originally Posted by Prove It
OK first of all, I doubt you could have written the question correctly. Should the second lot of brackets start with -16t^2?

Yes, I am sorry for that. ....-(-16t^2...
• Aug 22nd 2011, 07:17 PM
StudentMCCS
Re: Simplify ......
Thanks!
• Aug 22nd 2011, 07:35 PM
Prove It
Re: Simplify ......
Quote:

Originally Posted by StudentMCCS
Yes, I am sorry for that. ....-(-16t^2...

Quacky's post shows the solution with the fixed sign :)