$\begin{array}{l} \left( {\dfrac{1}{{\sqrt x - 2}} - \dfrac{{\sqrt x }}{{x - 4}}} \right):\dfrac{1}{{\sqrt x + 2}}\\ = \dfrac{{\sqrt x + 2 - \sqrt x }}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}}.\dfrac{{\sqrt x + 2}}{1}\\ = \dfrac{2}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}}.\dfrac{{\sqrt x + 2}}{1} = \dfrac{2}{{\sqrt x - 2}} \end{array}$
