Answer
$\frac{-6x-10}{(x+4)(x-3)}$
Work Step by Step
$\frac{x+2}{x+4} - \frac{x+1}{x-3}$
$\frac{(x+2)}{(x+4)}*(x-3)/(x-3) - \frac{(x+1)}{(x-3)}*(x+4)/(x+4)$
$\frac{(x+2)(x-3)}{(x+4)(x-3)}- \frac{(x+1)(x+4)}{(x-3)(x+4)}$
$\frac{(x^2-x-6)}{(x+4)(x-3)}- \frac{(x^2+5x+4)}{(x-3)(x+4)}$
$\frac{(x^2-x-6)-x^2-5x-4}{(x+4)(x-3)}$
$\frac{-6x-10}{(x+4)(x-3)}$