Answer
$\frac{5+\sqrt{3}}{22}$
Work Step by Step
We simplify the fraction by multiplying through by $5+\sqrt{3}$ and using the fact that $(a-b)(a+b)=a^2-b^2$:
$\displaystyle \frac{1}{5-\sqrt{3}}=\frac{1}{5-\sqrt{3}} \displaystyle \frac{5+\sqrt{3}}{5+\sqrt{3}}=\frac{5+\sqrt{3}}{25-3}=\frac{5+\sqrt{3}}{22}$
