Question

\(\left(\dfrac{a\sqrt{b}+b\sqrt{a}}{\sqrt{a}+\sqrt{b}}+\dfrac{a\sqrt{a}-b\sqrt{a}}{\sqrt{a}-\sqrt{b}}\right)\cdot\left(\dfrac{a-b}{\sqrt{a}-\sqrt{b}}\right)^2\)

Answer 1

\(=\left(\sqrt{ab}+\sqrt{a}\left(\sqrt{a}+\sqrt{b}\right)\right)\cdot\left(\dfrac{1}{\sqrt{a}+\sqrt{b}}\right)^2\)

\(=\left(a+2\sqrt{ab}\right)\cdot\dfrac{1}{a+2\sqrt{ab}+b}=\dfrac{a+2\sqrt{ab}}{a+2\sqrt{ab}+b}\)