Question 152379
To answer your questions...NO! and NO!  Let's look at the problem:
Simplify:
{{{(2x^2+2x-12)/(x^3+3x^2-4x-12)}}}
Let's do the numerator first: Factor the trinomial:
{{{2x^2+2x-12 = 2(x^2+x-6)}}} = {{{highlight(2(x+3)(x-2))}}} Your work in this step was ok!
Now the denominator: Factor:
{{{x^3+3x^2-4x-12 = (x^2-4)(x+3)}}}={{{highlight((x+2)(x-2)(x+3))}}} You correct here as well!
Now we'll put 'em together:
{{{(2(x+3)(x-2))/((x+2)(x-2)(x+3))}}} At this point, can you see the cancellation possibilities?
{{{(2(cross((x+3))cross((x-2))))/((x+2)cross((x-2))cross((x+3)))}}} = {{{highlight(2/(x+2))}}}