Pre Calculus Expression The questions is:
$$\dfrac{3(x+2)^2(x-3)^2 - 2(x+2)^3(x-3)}{(x-3)^4}$$
My answer is: $$\dfrac{3(x+2)^2 + 6x^2-4}{(x-3)^2}$$
Am I right? If not, where have I failed? 

Trusty maxima tells me:
factor(ratsimp((3*(x + 2)^2 * (x - 3)^2 - 2 * (x + 2)^3 * (x - 3))/(x - 3)^4));

is:
$$
\frac{(x - 13) (x + 2)^2}{(x - 3)^3}
$$
A trick that helps catch silly errors while simplifying is to replace some simple values, like $x = 0$ and $x = \pm 1$ in the expresssions.
