$$\frac{x^{2}-y^{2}}{x+y}\div\frac{x-y}{x+y}$$
$x+y$
$$\frac{\left(x^{2}-y^{2}\right)\left(x+y\right)}{\left(x+y\right)\left(x-y\right)}$$
$$\frac{x^{2}-y^{2}}{x-y}$$
$$\frac{\left(x+y\right)\left(x-y\right)}{x-y}$$
$$x+y$$
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