Answer
$\frac{5}{(x-4)(x+3)(x+1)}$
Work Step by Step
We multiply by $(x-4)(x+1)$, distribute and simplify:
$\displaystyle \frac{\frac{x-3}{x-4}-\frac{x+2}{x+1}}{x+3}=\frac{(x-3)(x+1)-(x+2)(x-4)}{(x-4)(x+3)(x+1)}=\frac{x^{2}-2x-3-(x^{2}-2x-8)}{(x-4)(x+3)(x+1)}=\frac{5}{(x-4)(x+3)(x+1)}$
