$$\frac{x^{4}-y^{4}}{x^{2}-2xy+y^{2}}\times\frac{x-y}{x(x+y)}\div\frac{x^{2}+y^{2}}{x}$$
$1$
$$\frac{\frac{\left(x+y\right)\left(x-y\right)\left(x^{2}+y^{2}\right)}{\left(x-y\right)^{2}}\times \frac{x-y}{x\left(x+y\right)}}{\frac{x^{2}+y^{2}}{x}}$$
$$\frac{\frac{\left(x+y\right)\left(x^{2}+y^{2}\right)}{x-y}\times \frac{x-y}{x\left(x+y\right)}}{\frac{x^{2}+y^{2}}{x}}$$
$$\frac{\frac{\left(x+y\right)\left(x^{2}+y^{2}\right)\left(x-y\right)}{\left(x-y\right)x\left(x+y\right)}}{\frac{x^{2}+y^{2}}{x}}$$
$$\frac{\frac{x^{2}+y^{2}}{x}}{\frac{x^{2}+y^{2}}{x}}$$
$$\frac{\left(x^{2}+y^{2}\right)x}{x\left(x^{2}+y^{2}\right)}$$
$$1$$
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