3 2 6 + 3 - 2 6 3 + 1 + 2 3 6 + 2 is equal to = ?

Answer: Option C

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