22. Упростите выражение $$(\frac{\sqrt{a}}{\sqrt{a}-\sqrt{b}}-\frac{\sqrt{b}}{\sqrt{a}+\sqrt{b}}):\frac{a-b}{a^{2}+ab}$$

Упростим выражение.

$$(\frac{\sqrt{a}}{\sqrt{a}-\sqrt{b}}-\frac{\sqrt{b}}{\sqrt{a}+\sqrt{b}}):\frac{a-b}{a^{2}+ab} = \frac{\sqrt{a}(\sqrt{a}+\sqrt{b})-\sqrt{b}(\sqrt{a}-\sqrt{b})}{(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b})}:\frac{a-b}{a(a+b)} = \frac{a+\sqrt{ab}-\sqrt{ab}+b}{a-b}:\frac{a-b}{a(a+b)} = \frac{a+b}{a-b}:\frac{a-b}{a(a+b)} = \frac{a+b}{a-b}\cdot\frac{a(a+b)}{a-b} = \frac{a(a+b)^{2}}{(a-b)^{2}}$$.

Ответ: $$\frac{a(a+b)^{2}}{(a-b)^{2}}$$.