Question

(√6-√2)/(1-√3)-5/√5):1/(√5-√2)

Answer 1

\(=\left(-\sqrt{2}-\sqrt{5}\right)\cdot\left(\sqrt{5}-\sqrt{2}\right)\)

\(=-\left(\sqrt{5}+\sqrt{2}\right)\cdot\left(\sqrt{5}-\sqrt{2}\right)\)

=-3

Answer 2

\(\dfrac{\sqrt{6}-\sqrt{2}}{1-\sqrt{3}}-\dfrac{5}{\sqrt{5}}:\dfrac{1}{\sqrt{5}-\sqrt{2}}\)

\(=\dfrac{-\sqrt{2}\left(\sqrt{3}-1\right)}{\sqrt{3}-1}-\dfrac{\sqrt{5}\cdot\sqrt{5}}{\sqrt{5}}:\dfrac{1}{\sqrt{5}-\sqrt{2}}\)

\(=-\sqrt{2}-\sqrt{5}\cdot\left(\sqrt{5}-\sqrt{2}\right)\)

\(=-\sqrt{2}-5+\sqrt{10}\)