# How do you simplify (sqrt(3) - 1)/(1+sqrt(3))?

Mar 15, 2018

$2 - \sqrt{3}$

#### Explanation:

(sqrt(3)-1)/(1+sqrt(3)=$\frac{- 1 + \sqrt{3}}{1 + \sqrt{3}}$

= $\frac{- 1 + \sqrt{3}}{1 + \sqrt{3}} . \frac{1 - \sqrt{3}}{1 - \sqrt{3}}$

= $\frac{- 1 + 2 \sqrt{3} - 3}{1 - 3}$= $\frac{2 \sqrt{3} - 4}{- 2}$
= $2 - \sqrt{3}$