$$\frac{x^{2}-1}{x^{2}+5x+6}*\frac{x+2}{x+1}$$
$\frac{x-1}{x+3}$
$$\frac{\left(x^{2}-1\right)\left(x+2\right)}{\left(x^{2}+5x+6\right)\left(x+1\right)}$$
$$\frac{\left(x-1\right)\left(x+1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}$$
$$\frac{x-1}{x+3}$$
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