2 + 6 3 + 12 + 3 + 1 3 - 2 equals to

Answer: Option D

$$\begin{array}{rl}& 2+\frac{6}{\sqrt{3}}+\frac{1}{2+\sqrt{3}}+\frac{1}{\sqrt{3}-2}\\ & \Rightarrow 2+\frac{2\times 3\sqrt{3}}{\sqrt{3}\times \sqrt{3}}+\frac{1}{2+\sqrt{3}}-\frac{1}{2-\sqrt{3}}\\ & \Rightarrow 2+2\sqrt{3}+\left(\frac{\left(2-\sqrt{3}\right)-\left(2+\sqrt{3}\right)}{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}\right)\\ & \Rightarrow 2+2\sqrt{3}+\left(\frac{2-\sqrt{3}-2-\sqrt{3}}{4-3}\right)\\ & \Rightarrow 2+2\sqrt{3}-2\sqrt{3}\\ & \Rightarrow 2\end{array}$$