If $$2 + x\sqrt 3 $$   = $$\frac{1}{{2 + \sqrt 3 }}{\text{,}}$$   then the simplest value of x is?

$$\eqalign{ & {\text{If }}2 + x\sqrt 3 = \frac{1}{{2 + \sqrt 3 }} \cr & {\text{Find }}x = ? \cr & \Rightarrow 2 + x\sqrt 3 = \frac{1}{{2 + \sqrt 3 }} \cr & \Rightarrow 2 + x \times \sqrt 3 = \frac{{2 - \sqrt 3 }}{1} \cr & \Rightarrow 2 + x\sqrt 3 = 2 - \sqrt 3 \cr & \Rightarrow x = - 1 \cr} $$