Answer
$\dfrac{1}{5-\sqrt{3}}=\dfrac{5+\sqrt{3}}{22}$
Work Step by Step
$\dfrac{1}{5-\sqrt{3}}$
Multiply both numerator and denominator by $5+\sqrt{3}$ and simplify:
$\dfrac{1}{5-\sqrt{3}}=\Big(\dfrac{1}{5-\sqrt{3}}\Big)\Big(\dfrac{5+\sqrt{3}}{5+\sqrt{3}}\Big)=\dfrac{5+\sqrt{3}}{5^{2}-(\sqrt{3})^{2}}=...$
$...=\dfrac{5+\sqrt{3}}{25-3}=\dfrac{5+\sqrt{3}}{22}$
