# How do you rationalize the denominator and simplify (6sqrt3 - sqrt7) /( 4 - sqrt3)?

Nov 19, 2017

$\frac{\left(4 + \sqrt{3}\right) \left(6 \sqrt{3} - \sqrt{7}\right)}{13}$
$\frac{6 \sqrt{3} - \sqrt{7}}{4 - \sqrt{3}} = \frac{6 \sqrt{3} - \sqrt{7}}{4 - \sqrt{3}} \left(\frac{4 + \sqrt{3}}{4 + \sqrt{3}}\right)$
$= \frac{\left(4 + \sqrt{3}\right) \left(6 \sqrt{3} - \sqrt{7}\right)}{16 - 3}$
$= \frac{\left(4 + \sqrt{3}\right) \left(6 \sqrt{3} - \sqrt{7}\right)}{13}$