\[\frac{1}{\sqrt{6} - \sqrt{3}} =\]
\[= \frac{\sqrt{6} + \sqrt{3}}{\left( \sqrt{6} - \sqrt{3} \right)\left( \sqrt{6} + \sqrt{3} \right)} =\]
\[= \frac{\sqrt{6} + \sqrt{3}}{6 - 3} = \frac{\sqrt{6} + \sqrt{3}\ }{3}\]