Answer
$\frac{11 (\sqrt 7 +\sqrt 3 )}{4}$ (or) $\frac{11}{4} (\sqrt 7 + \sqrt 3)$
Work Step by Step
$ \frac{11}{(\sqrt 7 - \sqrt 3)}$
The conjugate of the denominator is $ \sqrt 7 + \sqrt 3 $. Multiply the denominator and numerator by $ \sqrt 7 + \sqrt 3 $, so the simplified denominator will not contain a radical. Therefore, multiply by 1, choosing $\frac{ \sqrt 7 + \sqrt 3 .}{ \sqrt 7 + \sqrt 3 .}$ for 1.
$ \frac{11}{(\sqrt 7 - \sqrt 3)}$ = $ \frac{11}{(\sqrt 7 - \sqrt 3)}$ $\times$ $\frac{ \sqrt 7 + \sqrt 3 .}{ \sqrt 7 + \sqrt 3 .}$
= $ \frac{11 ( \sqrt 7 + \sqrt 3 ) }{( \sqrt 7 - \sqrt 3 )( \sqrt 7 + \sqrt 3 )}$
$( \sqrt a - \sqrt b)( \sqrt a + \sqrt b)$ = $ (\sqrt a)^{2}$ - $ (\sqrt b)^{2}$. Therefore,
$( \sqrt 7 - \sqrt 3)( \sqrt7 +\sqrt 3)$ = $ (\sqrt7)^{2}$ - $ (\sqrt 3)^{2}$.
= $ \frac{11 ( \sqrt7 + \sqrt 3 ) }{(\sqrt7)^{2} - (\sqrt 3)^{2}}$
= $ \frac{11 ( \sqrt7 + \sqrt 3 ) }{ 7- 3}$
= $ \frac{11 ( \sqrt7 + \sqrt 3 ) }{ 4}$ (or) $\frac{11}{4} (\sqrt 7 + \sqrt 3)$
