Answer
$\dfrac{3(x+2)^{2}(x-3)^{2}-(x+2)^{3}(2)(x-3)}{(x-3)^{4}}=\dfrac{(x+2)^{2}(x-13)}{(x-3)^{3}}$
Work Step by Step
$\dfrac{3(x+2)^{2}(x-3)^{2}-(x+2)^{3}(2)(x-3)}{(x-3)^{4}}$
Take out common factor $(x+2)^{2}(x-3)$ from the numerator:
$\dfrac{3(x+2)^{2}(x-3)^{2}-(x+2)^{3}(2)(x-3)}{(x-3)^{4}}=...$
$...=\dfrac{(x+2)^{2}(x-3)[3(x-3)-2(x+2)]}{(x-3)^{4}}=...$
Simplify the expression inside brackets in the numerator:
$...=\dfrac{(x+2)^{2}(x-3)[3x-9-2x-4]}{(x-3)^{4}}=...$
$...=\dfrac{(x+2)^{2}(x-3)(x-13)}{(x-3)^{4}}=...$
Simplify the rational expression:
$...=\dfrac{(x+2)^{2}(x-13)}{(x-3)^{3}}$
