Question

\(\dfrac{ab}{\sqrt{b}}-a\sqrt{\dfrac{b}{a}}+b\sqrt{\dfrac{a}{b}}-\dfrac{ab}{\sqrt{a}}\)

Answer 1

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