# How do you rationalize the following problem 1/ (1+ square root of 3 - square root of 5)?

Sep 16, 2015

$- \frac{\sqrt{3} + \sqrt{5}}{2}$
$\frac{1}{\sqrt{3} - \sqrt{5}} = \frac{1}{\sqrt{3} - \sqrt{5}} \frac{\sqrt{3} + \sqrt{5}}{\sqrt{3} + \sqrt{5}} =$
$= \frac{\sqrt{3} + \sqrt{5}}{{\left(\sqrt{3}\right)}^{2} - {\left(\sqrt{5}\right)}^{2}} = \frac{\sqrt{3} + \sqrt{5}}{3 - 5} =$
$= \frac{\sqrt{3} + \sqrt{5}}{-} 2 = - \frac{\sqrt{3} + \sqrt{5}}{2}$