7. Упростите выражение: xy/√x-√y⋅(√x-2√y/√xy+1/√x)

$$\frac{xy}{\sqrt{x} - \sqrt{y}} \cdot (\frac{\sqrt{x} - 2\sqrt{y}}{\sqrt{xy}} + \frac{1}{\sqrt{x}}) = \frac{xy}{\sqrt{x} - \sqrt{y}} \cdot (\frac{\sqrt{x} - 2\sqrt{y}}{\sqrt{x}\sqrt{y}} + \frac{\sqrt{y}}{\sqrt{x}\sqrt{y}}) = \frac{xy}{\sqrt{x} - \sqrt{y}} \cdot \frac{\sqrt{x} - 2\sqrt{y} + \sqrt{y}}{\sqrt{x}\sqrt{y}} = \frac{xy}{\sqrt{x} - \sqrt{y}} \cdot \frac{\sqrt{x} - \sqrt{y}}{\sqrt{x}\sqrt{y}} = \frac{xy}{\sqrt{x}\sqrt{y}} = \frac{\sqrt{xy} \cdot \sqrt{xy}}{\sqrt{x}\sqrt{y}} = \sqrt{xy}$$ Ответ: $$\sqrt{xy}$$