Answer
$\frac{(x+2)^{2}(x-13)}{(x-3)^{3}}$
Work Step by Step
We factor out the $(x+2)$ and $(x-3)$ terms and then simplify:
$\displaystyle \frac{3(x+2)^{2}(x-3)^{2}-(x+2)^{3}(2)(x-3)}{(x-3)^{4}}=\frac{(x+2)^{2}(x-3)[3(x-3)-(x+2)(2)]}{(x-3)^{4}}
=\frac{(x+2)^{2}(3x-9-2x-4)}{(x-3)^{3}}=\frac{(x+2)^{2}(x-13)}{(x-3)^{3}}$
