Question

Tính:
a) \(\frac{3}{\sqrt{5}+\sqrt{2}}+\frac{1}{\sqrt{2}-1}-\frac{4}{3-\sqrt{5}}\)
b) \(\frac{1}{2+\sqrt{3}}+\frac{\sqrt{2}}{\sqrt{6}}-\frac{3}{3+\sqrt{3}}\)

Answer 1

\(A=\frac{3\left(\sqrt{5}-\sqrt{2}\right)}{\left(\sqrt{5}-\sqrt{2}\right)\left(\sqrt{5}+\sqrt{2}\right)}+\frac{\sqrt{2}+1}{\left(\sqrt{2}+1\right)\left(\sqrt{2}-1\right)}-\frac{4\left(3+\sqrt{5}\right)}{\left(3+\sqrt{5}\right)\left(3-\sqrt{5}\right)}\)

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

\(=1-3=-2\)

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

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

\(=\frac{3-\sqrt{3}}{6}\)