Решение:

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

Ответ: $$\frac{x}{y}$$