21. Упростите выражение $$(\frac{\sqrt{m}}{n-\sqrt{mn}}+\frac{\sqrt{n}}{m-\sqrt{mn}})\cdot\frac{\sqrt{mn}}{\sqrt{n}+\sqrt{m}}$$

Упростим выражение.

$$(\frac{\sqrt{m}}{n-\sqrt{mn}}+\frac{\sqrt{n}}{m-\sqrt{mn}})\cdot\frac{\sqrt{mn}}{\sqrt{n}+\sqrt{m}} = (\frac{\sqrt{m}}{\sqrt{n}(\sqrt{n}-\sqrt{m})}+\frac{\sqrt{n}}{\sqrt{m}(\sqrt{m}-\sqrt{n})})\cdot\frac{\sqrt{mn}}{\sqrt{n}+\sqrt{m}} = (\frac{\sqrt{m}}{\sqrt{n}(\sqrt{n}-\sqrt{m})}-\frac{\sqrt{n}}{\sqrt{m}(\sqrt{n}-\sqrt{m})})\cdot\frac{\sqrt{mn}}{\sqrt{n}+\sqrt{m}} = \frac{m-n}{\sqrt{mn}(\sqrt{n}-\sqrt{m})}\cdot\frac{\sqrt{mn}}{\sqrt{n}+\sqrt{m}} = \frac{m-n}{-(\sqrt{m}-\sqrt{n})(\sqrt{n}+\sqrt{m})} = \frac{m-n}{-(n-m)} = \frac{m-n}{m-n} = -1$$.

Ответ: -1