Answer
$\frac{-1}{\sqrt{3}-\sqrt{5}}$
Work Step by Step
We simplify the fraction by multiplying through by $\sqrt{3}-\sqrt{5}$ and using the fact that $(a-b)(a+b)=a^2-b^2$:
$\displaystyle \frac{\sqrt{3}+\sqrt{5}}{2}=\frac{\sqrt{3}+\sqrt{5}}{2}*\displaystyle \frac{\sqrt{3}-\sqrt{5}}{\sqrt{3}-\sqrt{5}}=\frac{3-5}{2(\sqrt{3}-\sqrt{5})}=\frac{-2}{2(\sqrt{3}-\sqrt{5})}=\frac{-1}{\sqrt{3}-\sqrt{5}}$
