Question

Rút gọn:

a;\(\frac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}\)+\(\frac{5-2\sqrt{5}}{2\sqrt{5}-4}\)

b;\(\frac{5+\sqrt{5}}{\sqrt{10}+\sqrt{2}}\)

Answer 1

a) Ta có: \(\frac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}+\frac{5-2\sqrt{5}}{2\sqrt{5}-4}\)

\(=\frac{\sqrt{5}\left(\sqrt{3}-1\right)}{\sqrt{3}-1}+\frac{\sqrt{5}\left(\sqrt{5}-2\right)}{2\left(\sqrt{5}-2\right)}\)

\(=\sqrt{5}-\frac{\sqrt{5}}{2}=\frac{2\sqrt{5}}{2}-\frac{\sqrt{5}}{2}=\frac{\sqrt{5}}{2}\)

b) Ta có: \(\frac{5+\sqrt{5}}{\sqrt{10}+\sqrt{2}}\)

\(=\frac{\sqrt{5}\left(\sqrt{5}+1\right)}{\sqrt{2}\left(\sqrt{5}+1\right)}\)

\(=\frac{\sqrt{5}}{\sqrt{2}}\)