Question

simplify 6/2 root 3 - root 6 + root 6/root 3 + root 2 - 4 root 3 /root 6- root 2​

Answer 1

$$\begin{gathered} \frac{6}{2\sqrt{3}-\sqrt{6}}+\frac{\sqrt{6}}{\sqrt{3}+\sqrt{2}}-\frac{4\sqrt{3}}{\sqrt{6}-\sqrt{2}} \\ =\frac{6}{2\sqrt{3}-\sqrt{6}}\times \frac{2\sqrt{3}+\sqrt{6}}{2\sqrt{3}+\sqrt{6}}+\frac{\sqrt{6}}{\sqrt{3}+\sqrt{2}}\times \frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2}}-\frac{4\sqrt{3}}{\sqrt{6}-\sqrt{2}}\times \frac{\sqrt{6}+\sqrt{2}}{\sqrt{6}+\sqrt{2}} \\ =\frac{6\left(2\sqrt{3}+\sqrt{6}\right)}{12-6}+\frac{\sqrt{18}-\sqrt{12}}{3-2}-\frac{4\left(\sqrt{18}+\sqrt{6}\right)}{6-2} \\ =\frac{6\left(2\sqrt{3}+\sqrt{6}\right)}{6}+\frac{\sqrt{18}-\sqrt{12}}{1}-\frac{4\left(\sqrt{18}+\sqrt{6}\right)}{4} \\ =2\sqrt{3}+\sqrt{6}+3\sqrt{2}-2\sqrt{3}-3\sqrt{2}-\sqrt{6} \\ =0 \end{gathered}$$