SOLUTION: I am working on this problem and I just need to know if I did it right. I'm suppose to simplify each expression an if an expression can't be simplified, write "does not simplify.

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Question 152379This question is from textbook Intermediate Algebra
: I am working on this problem and I just need to know if I did it right.
I'm suppose to simplify each expression an if an expression can't be simplified, write "does not simplify.
The problem is 2x^2+2x-12 over x^3+3x^2-4x-12
This is what I did
Factored to 2(x^2+x-6)
Factored to 2(x^2+3x-2x-6)
Factored to 2(x(x+3)-2(x+3))
Factored to 2(x+3)(x-2) also common denominator
2x(x-2)+2*3(x-2)
Simplified to 2x(x-2)+6(x-2)
Factored to 2(x-2)(x+3)
Second part denominator :
Factored to x^2(x+3)-4(x+3)
Factored to (x+3)(x^2-4)
Factored to (x+3)(x+2)(x-2) also common denominator
Expanded x(x+2)(x-2)+3(x+2)(x-2) also simplified
Factored to (x+2)(x-2)(x+3) also simplified
Now the answer I got was 2x(x-2)+6(x-2) over (x-2)(x+3)(x+2). Was this problem done correctly and is it simplified?
Thanks for anyone who can check this. This question is from textbook Intermediate Algebra

Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
To answer your questions...NO! and NO! Let's look at the problem:
Simplify:

Let's do the numerator first: Factor the trinomial:
= Your work in this step was ok!
Now the denominator: Factor:
= You correct here as well!
Now we'll put 'em together:
At this point, can you see the cancellation possibilities?
=