Answer
$-1$
Work Step by Step
$\frac{(x+1)^{2}(x+2)^{3}-(x+1)^{3}(x+2)^{2}}{(x+2)^{2}}=0$
$\frac{(x+1)^{2}(x+2)^{2}-(x+2-x-1)}{(x+2)^{2}}=0$
$\frac{(x+1)^{2}(x+2)^{2}}{(x+2)^{2}}=0$
$x=-1$
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