Question

\(\frac{5\sqrt{3}}{\sqrt{3-\sqrt{5}}-\sqrt{3}}-\frac{5\sqrt{3}}{\sqrt{3-\sqrt{5}}+\sqrt{3}}\)

\(\frac{a}{a-2\sqrt{b}}\)

\(\frac{\sqrt{b}+b\sqrt{a}}{\sqrt{a}+\sqrt{b}}\)

Answer 1

\(\frac{5\sqrt{3}}{\sqrt{3-\sqrt{5}}-\sqrt{3}}-\frac{5\sqrt{3}}{\sqrt{3-\sqrt{5}}+\sqrt{3}}\)

\(=\frac{5\sqrt{3}\left(\sqrt{3-\sqrt{5}}+\sqrt{3}\right)-5\sqrt{3}\left(\sqrt{3-\sqrt{5}}-\sqrt{3}\right)}{\left(\sqrt{3-\sqrt{5}}-\sqrt{3}\right)\left(\sqrt{3-\sqrt{5}}+\sqrt{3}\right)}\)

\(=\frac{5\sqrt{3}.2\sqrt{3}}{3-\sqrt{5}-3}=-\frac{30}{\sqrt{5}}=-\frac{\sqrt{5}.\sqrt{180}}{\sqrt{5}}=-\sqrt{180}\)