Answer
$10-5\sqrt{3}$
Work Step by Step
Given \begin{equation}
\frac{5}{2+\sqrt{3}}.
\end{equation} Simplify by rationalizing the denominator.
\begin{equation}
\begin{aligned}
\frac{5}{2+\sqrt{3}}&=\frac{5}{2+\sqrt{3}}\cdot \frac{\left( 2-\sqrt{3}\right) }{\left( 2-\sqrt{3}\right) }\\
& =\frac{5 \left( 2-\sqrt{3}\right)}{4-3}\\
&= 5\left( 2-\sqrt{3}\right)\\
&= 10-5\sqrt{3}.
\end{aligned}
\end{equation}
