\[\frac{\sqrt{a}}{\sqrt{\text{ab}} + b} - \frac{\sqrt{b}}{a + \sqrt{\text{ab}}} =\]
\[= \frac{\left( \sqrt{a} \right)^{2} - \left( \sqrt{b} \right)^{2}}{\sqrt{\text{ab}}\left( \sqrt{a} + \sqrt{b} \right)} =\]
\[= \frac{a - b}{\sqrt{\text{ab}}\left( \sqrt{a} + \sqrt{b} \right)} =\]
\[= \frac{\sqrt{a} - \sqrt{b}}{\sqrt{\text{ab}}}\]