If 2 + x 3 = 12 + 3 , then the simplest value of x is?

Answer: Option D

$$\begin{array}{rl}& \text{If }2+x\sqrt{3}=\frac{1}{2+\sqrt{3}}\\ & \text{Find }x=?\\ & \Rightarrow 2+x\sqrt{3}=\frac{1}{2+\sqrt{3}}\\ & \Rightarrow 2+x\times \sqrt{3}=\frac{2-\sqrt{3}}{1}\\ & \Rightarrow 2+x\sqrt{3}=2-\sqrt{3}\\ & \Rightarrow x=-1\end{array}$$