$$\frac{x^{2}+x}{x^{2}-y^{2}}\times\frac{xy-y^{2}}{x+1}$$
$\frac{xy}{x+y}$
$$\frac{\left(x^{2}+x\right)\left(xy-y^{2}\right)}{\left(x^{2}-y^{2}\right)\left(x+1\right)}$$
$$\frac{xy\left(x+1\right)\left(x-y\right)}{\left(x+1\right)\left(x+y\right)\left(x-y\right)}$$
$$\frac{xy}{x+y}$$
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