( 1 + 2 5 + 3 + 1 - 2 5 - 3 ) simplifies to = ?

Answer: Option C

$$\frac{1+\sqrt{2}}{\sqrt{5}+\sqrt{3}}+\frac{1-\sqrt{2}}{\sqrt{5}-\sqrt{3}}$$
$$\Rightarrow \frac{\left(1+\sqrt{2}\right)\left(\sqrt{5}-\sqrt{3}\right)+\left(1-\sqrt{2}\right)\left(\sqrt{5}+\sqrt{3}\right)}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}$$
$$\Rightarrow \frac{\sqrt{5}-\sqrt{3}+\sqrt{10}-\sqrt{6}+\sqrt{5}+\sqrt{3}-\sqrt{10}-\sqrt{6}}{5-3}$$
$$\begin{array}{rl}& \Rightarrow \frac{2\sqrt{5}-2\sqrt{6}}{2}\\ & \Rightarrow \frac{2\left(\sqrt{5}-\sqrt{6}\right)}{2}\\ & \Rightarrow \sqrt{5}-\sqrt{6}\end{array}$$