# How do you simplify 5/(-5-3sqrt3)?

Jun 22, 2017

See a solution process below:

#### Explanation:

To simplify the expression we need to rationalize the denominator:

$\frac{5}{- 5 - 3 \sqrt{3}} \times \frac{- 5 + 3 \sqrt{3}}{- 5 + 3 \sqrt{3}} \implies \frac{- 25 + 15 \sqrt{3}}{25 - 15 \sqrt{3} + 15 \sqrt{3} - 9 {\left(\sqrt{3}\right)}^{2}} \implies$

$\frac{- 25 + 15 \sqrt{3}}{25 - 0 - \left(9 \cdot 3\right)} \implies \frac{- 25 + 15 \sqrt{3}}{25 - 27} \implies$

$\frac{- 25 + 15 \sqrt{3}}{-} 2$

Or

$\frac{25}{2} - \frac{15}{2} \sqrt{3}$