Question

Answer 1

\(=\dfrac{\sqrt{a}}{a-b}3\sqrt{\left(\sqrt{a}-\sqrt{b}\right)^2}+\dfrac{3\sqrt{b}\left(\sqrt{a}-\sqrt{b}\right)}{a-b}\)

\(=\dfrac{3\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)}{a-b}+\dfrac{3\sqrt{b}\left(\sqrt{a}-\sqrt{b}\right)}{a-b}\)

\(=\dfrac{3a-3\sqrt{ab}+3\sqrt{ab}-3b}{a-b}=\dfrac{3\left(a-b\right)}{a-b}=3\)

Answer 2

\(\dfrac{\sqrt{a}}{a-b}\cdot\sqrt{9\left(a-2\sqrt{ab}+b\right)}+\dfrac{3\sqrt{a}}{\sqrt{a}+\sqrt{b}}\)

\(=\dfrac{3\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)}{a-b}+\dfrac{3\sqrt{a}}{\sqrt{a}+\sqrt{b}}\)

\(=\dfrac{6\sqrt{a}}{\sqrt{a}+\sqrt{b}}\)