$\begin{array}{l} \dfrac{{\sqrt a }}{{\sqrt a - \sqrt b }} - \dfrac{{\sqrt b }}{{\sqrt a + \sqrt b }}\\ = \dfrac{{\sqrt a \left( {\sqrt a + \sqrt b } \right) - \sqrt b \left( {\sqrt a - \sqrt b } \right)}}{{\left( {\sqrt a - \sqrt b } \right)\left( {\sqrt a + \sqrt b } \right)}}\\ = \dfrac{{a + \sqrt {ab} - \sqrt {ab} + b}}{{a - b}}\\ = \dfrac{{a + b}}{{a - b}} \end{array}$
