Question

Answer 1

\(M=\left(\dfrac{\sqrt{a}+\sqrt{b}}{\sqrt{a}-\sqrt{b}}-\dfrac{4\sqrt{ab}}{a-b}\right)\cdot\dfrac{a\sqrt{a}+b\sqrt{a}}{\sqrt{ab}-\left(a+b\right)}\)

\(=\left(\dfrac{\sqrt{a}+\sqrt{b}}{\sqrt{a}-\sqrt{b}}-\dfrac{4\sqrt{ab}}{\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}\right)\cdot\dfrac{\sqrt{a}\left(a+b\right)}{\sqrt{ab}-a-b}\)

\(=\dfrac{\left(\sqrt{a}+\sqrt{b}\right)^2-4\sqrt{ab}}{\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)}\cdot\dfrac{\sqrt{a}\left(a+b\right)}{\sqrt{ab}-a-b}\)

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

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