Question

Tính 

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

b) \(\frac{1}{2+\sqrt{3}}+\frac{\sqrt{2}}{\sqrt{6}}-\frac{4}{3+\sqrt{3}}\)

Answer 1

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

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

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

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

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

Answer 2

\(\frac{1}{2+\sqrt{3}}+\frac{\sqrt{2}}{\sqrt{6}}-\frac{4}{3+\sqrt{3}}\)

\(=\frac{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}{2+\sqrt{3}}+\frac{1}{\sqrt{3}}-\frac{4}{3+\sqrt{3}}\)

\(=2-\sqrt{3}+\frac{1}{\sqrt{3}}-\frac{4}{3+\sqrt{3}}\)