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