Question

Tính

A=\(\dfrac{5+3\sqrt{5}}{\sqrt{5}}+\dfrac{3+\sqrt{3}}{\sqrt{3}+1}-\left(\sqrt{5}+3\right)\)

B=\(\dfrac{30}{\sqrt{6}+1}+\dfrac{2}{\sqrt{6}-2}-\dfrac{6}{3-\sqrt{6}}\)

Answer 1

\(A=\dfrac{\sqrt{5}\left(\sqrt{5}+3\right)}{\sqrt{5}}+\dfrac{\sqrt{3}\left(\sqrt{3}+1\right)}{\sqrt{3}+1}-\left(\sqrt{5}+3\right)\)
\(=\sqrt{5}+3+\sqrt{3}-\sqrt{5}-3=\sqrt{3}\)

Answer 2

\(B=\dfrac{30\left(\sqrt{6}-1\right)}{5}+\dfrac{2\left(\sqrt{6}+2\right)}{2}-\dfrac{6\left(3+\sqrt{6}\right)}{3}\)

\(=6\left(\sqrt{6}-1\right)+\sqrt{6}+2-2\left(3+\sqrt{6}\right)\)

\(=6\sqrt{6}-6+\sqrt{6}+2-2\sqrt{3}-2\sqrt{6}=5\sqrt{6}-4-2\sqrt{3}\)