Question

Thực hiện phép tính:
\(\frac{2}{\sqrt{6}-2}+\frac{2}{\sqrt{6}+2}+\frac{5}{\sqrt{6}}\)

Answer 1

\(\frac{2}{\sqrt{6}-2}+\frac{2}{\sqrt{6}+2}+\frac{5}{\sqrt{6}}\)

\(=\frac{2\left(\sqrt{6}+2\right)}{\left(\sqrt{6}-2\right)\left(\sqrt{6}+2\right)}+\frac{2\left(\sqrt{6}-2\right)}{\left(\sqrt{6}+2\right)\left(\sqrt{6}-2\right)}+\frac{5\sqrt{6}}{\sqrt{6}.\sqrt{6}}\)

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

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

\(=\frac{6\sqrt{6}+12+6\sqrt{6}-12+5\sqrt{6}}{6}\)

\(=\frac{17\sqrt{6}}{6}\)