Question

\(\dfrac{2-\sqrt{6}}{3\sqrt{3}-3}\)

Answer 1

\(\dfrac{2-\sqrt{6}}{3\sqrt{3}-3}\)

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

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

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

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

Answer 2

\(=\dfrac{\left(2-\sqrt{6}\right)\left(\sqrt{3}+1\right)}{3\cdot2}=\dfrac{2\sqrt{3}+2-3\sqrt{2}-\sqrt{6}}{6}\)