# How do you simplify (2-sqrt3)/(-2-sqrt5)?

Jul 9, 2017

See a solution process below:

#### Explanation:

First, we will rationalize the denominator to remove the radicals from the denominator by multiplying the expression by the necessary form or $1$:

$\frac{- 2 + \sqrt{5}}{- 2 + \sqrt{5}} \times \frac{2 - \sqrt{3}}{- 2 - \sqrt{5}} \implies$

$\frac{\left(- 2 \cdot 2\right) + 2 \sqrt{3} + 2 \sqrt{5} - \sqrt{5} \sqrt{3}}{\left(- 2 \cdot - 2\right) + 2 \sqrt{5} - 2 \sqrt{5} - \sqrt{5} \sqrt{5}} \implies$

$\frac{- 4 + 2 \sqrt{3} + 2 \sqrt{5} - \sqrt{15}}{4 + 0 - 5} \implies$

$\frac{- 4 + 2 \sqrt{3} + 2 \sqrt{5} - \sqrt{15}}{-} 1 \implies$

$4 - 2 \sqrt{3} - 2 \sqrt{5} + \sqrt{15}$

Or

$4 - 2 \left(\sqrt{3} + \sqrt{5}\right) + \sqrt{15}$