# where do I go from here?

G

#### Guest

##### Guest
t - 8
__ ____
t-2 t^2-4

I only go this far:

t - 8
___ ________
t-2 (t+4) (t-2)

Where do I go from here? As usual I am confused. :shock:

#### ChaoticLlama

##### Junior Member
I am assuming that the original problem looks like this

Code:
t  - 8
__  _____
t-2 t²-4
Factoring the denominator of the second term like so will help.

Note: The factoring that you showed is wrong.
t² - 4 does NOT equal (t+4)(t-2)
If you are ever wondering if you have factored it properly, check!
(t+4)(t-2) = t² + 4t - 2t - 8
................= t² + 2t - 8

The proper factoring of t² - 4 is (t+2)(t-2).
Check if you wish to prove it to yourself.

Code:
t  -     8
__  _________
t-2 (t+2)(t-2)
Then the common denominator is clear to see. It is (t+2)(t-2)
So what you must do now is multiply the first term by (t+2)/(t+2)

Note: Keep in mind that you are technically multiplying by 1, so you aren't really changing the term.

Code:
  t(t+2)  -  8
________   ________
(t-2)(t+2) (t+2)(t-2)
Can you take it from here?

G

Thanks

I will try!

#### Denis

##### Senior Member
[quote="ChaoticLlama
Code:
  t(t+2)  -  8
________   ________
(t-2)(t+2) (t+2)(t-2)
[/quote]

How you doing with that one, mom?

First, CL's equation above is (simplified):
t(t + 2) - 8
========
(t + 2)(t - 2)

complete the numerator:
t^2 + 2t - 8
========
(t + 2)(t - 2)

now factor the critter:
(t + 4)(t - 2)
========
(t + 2)(t - 2)

shoot them (t - 2)'s:
t + 4
====
t + 2

You also got that, right?

G

#### Guest

##### Guest
I am so happy

I finally got it! With your help I figured it out ! Thanks so much. I am a crazy mom! At least that is what my son calls me :?: