Answer
$-\displaystyle \frac{(11x+2)}{(x+2)(x-2)}$
Work Step by Step
$\displaystyle \frac{x-3}{x+2}-\frac{x+4}{x-2}=... \quad LCD=(x+2)(x-2)$
$=\displaystyle \frac{(x-3)(x-2)-(x+4)(x+2)}{(x+2)(x-2)}$
$=\displaystyle \frac{x^{2}-5x+6-(x^{2}+6x+8)}{(x+2)(x-2)}$
$=\displaystyle \frac{x^{2}-5x+6-x^{2}-6x-8}{(x+2)(x-2)}$
$=\displaystyle \frac{-11x-2}{(x-4)(x+3)}$
$=\displaystyle \frac{-(11x+2)}{(x-4)(x+3)}$
$=-\displaystyle \frac{(11x+2)}{(x+2)(x-2)}$
