Answer
$3 ( \sqrt 5 - \sqrt 3) $ or $ 3 \sqrt 5 - 3\sqrt 3$
Work Step by Step
$ \frac{6}{\sqrt 5 + \sqrt 3}$
The conjugate of the denominator is $ \sqrt 5 - \sqrt 3 $. Multiply the denominator and numerator by $ \sqrt 5 - \sqrt 3 $, so the simplified denominator will not contain a radical. Therefore, multiply by 1, choosing $\frac{ \sqrt 5 - \sqrt 3 .}{ \sqrt 5 - \sqrt 3 .}$ for 1.
$ \frac{6}{\sqrt 5 + \sqrt 3}$ = $ \frac{6}{\sqrt 5 + \sqrt 3}$ $\times$ $\frac{ \sqrt 5 - \sqrt 3 .}{ \sqrt 5 - \sqrt 3 .}$
= $ \frac{6 ( \sqrt 5 - \sqrt 3 ) }{( \sqrt 5 + \sqrt 3 )( \sqrt 5 - \sqrt 3 )}$
$( \sqrt a - \sqrt b)( \sqrt a + \sqrt b)$ = $ (\sqrt a)^{2}$ - $ (\sqrt b)^{2}$. Therefore,
$( \sqrt 5 - \sqrt 3)( \sqrt5 +\sqrt 3)$ = $ (\sqrt 5)^{2}$ - $ (\sqrt 3)^{2}$.
= $ \frac{6 ( \sqrt 5 - \sqrt 3 ) }{5 -3}$
= $ \frac{6 ( \sqrt 5 - \sqrt 3 ) }{2}$
= $\frac{6}{2} \times ( \sqrt 5 - \sqrt 3 ) $
= $ 3 ( \sqrt 5 - \sqrt 3 ) $ or $ 3\sqrt 5 - 3\sqrt 3$
