( 2+ 32- 3+ 2 - 32 + 3 + 3 - 1 3 + 1 ) Simplifies to :

Answer: Option C

$$\left(\frac{2+\sqrt{3}}{2-\sqrt{3}}+\frac{2-\sqrt{3}}{2+\sqrt{3}}+\frac{\sqrt{3}-1}{\sqrt{3}+1}\right)$$
$$=\left\{\frac{{\left(2+\sqrt{3}\right)}^2+{\left(2-\sqrt{3}\right)}^2}{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}+\frac{\sqrt{3}-1}{\sqrt{3}+1}\times \frac{\sqrt{3}-1}{\sqrt{3}-1}\right\}$$
$$=\left\{\frac{4+3+4\sqrt{3}+4+3-4\sqrt{3}}{4-3}+\frac{{\left(\sqrt{3}-1\right)}^2}{3-1}\right\}$$
$$\begin{array}{rl}& =\left\{14+\frac{3+1-2\sqrt{3}}{2}\right\}\\ & =14+\frac{2\left(2-\sqrt{3}\right)}{2}\\ & =14+2-\sqrt{3}\\ & =16-\sqrt{3}\end{array}$$