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Решите задачу:

$(\frac{a\sqrt{a}-b\sqrt{b}}{\sqrt{a}-\sqrt{b}}+\sqrt{ab}):(\sqrt{ab}(\frac{1}{\sqrt{a}}+\frac{1}{\sqrt{b}})=\frac{a\sqrt{a}-b\sqrt{b}+\sqrt{ab}(\sqrt{a}-\sqrt{b})}{\sqrt{a}-\sqrt{b}}:(\sqrt{ab}*\frac{\sqrt{b}+\sqrt{a}}{\sqrt{ab}})=\\\ \\\ =\frac{a\sqrt{a}-b\sqrt{b}+a\sqrt{b}-b\sqrt{a}}{\sqrt{a}-\sqrt{b}}:(\sqrt{a}+\sqrt{b})=\frac{a(\sqrt{a}+\sqrt{b})-b(\sqrt{a}+\sqrt{b})}{\sqrt{a}-\sqrt{b}}*\frac{1}{\sqrt{a}+\sqrt{b}}=\\\ \\\ =\frac{(a-b)(\sqrt{a}+\sqrt{b})}{(a-b)}=\sqrt{a}+\sqrt{b}$