Answer
$\frac{5 ( \sqrt3 + 1)}{2}$ or $\frac{5\sqrt3 + 5}{2}$
Work Step by Step
$ \frac{5}{(\sqrt 3 -1)}$
The conjugate of the denominator is $ \sqrt 3 + 1$. Multiply the denominator and numerator by $ \sqrt 3 + 1 $, so the simplified denominator will not contain a radical. Therefore, multiply by 1, choosing $\frac{ \sqrt 3 + 1}{ \sqrt 3 + 1}$ for 1.
= $ \frac{5}{(\sqrt 3 -1)}$ $ \times $ $ \frac{\sqrt 3 + 1}{(\sqrt 3+1)}$
= $ \frac{5 ( \sqrt 3 + 1 )}{ ( \sqrt 3 - 1 ) ( \sqrt 3 + 1 )}$
$( \sqrt a - \sqrt b)( \sqrt a + \sqrt b)$ = $ (\sqrt a)^{2}$ - $ (\sqrt b)^{2}$. Therefore,
$( \sqrt 3 - 1)( \sqrt3 + 1)$ = $ (\sqrt 3)^{2}$ - $ (1)^{2}$.
= $ \frac{5 ( \sqrt 3 + 1 )}{ (\sqrt 3)^{2} - (1)^{2}}$
= $ \frac{5 ( \sqrt 3 + 1 )}{ 3 - 1}$
= $ \frac{5 ( \sqrt 3 + 1 )}{2}$ or $\frac{5\sqrt3 + 5}{2}$
