$(\frac{\sqrt{a} - \sqrt{b}}{a + \sqrt{ab}} - \frac{1}{a - b} * \frac{(\sqrt{b} - \sqrt{a})^2}{\sqrt{a} + \sqrt{b}}) : \frac{\sqrt{a} - \sqrt{b}}{a + \sqrt{ab}} = (\frac{\sqrt{a} - \sqrt{b}}{\sqrt{a}(\sqrt{a} + \sqrt{b})} - \frac{1}{(\sqrt{a} - \sqrt{b})(\sqrt{a} + \sqrt{b})} * \frac{(\sqrt{a} - \sqrt{b})^2}{\sqrt{a} + \sqrt{b}}) : \frac{\sqrt{a} - \sqrt{b}}{\sqrt{a}(\sqrt{a} + \sqrt{b})} = (\frac{\sqrt{a} - \sqrt{b}}{\sqrt{a}(\sqrt{a} + \sqrt{b})} - \frac{1}{\sqrt{a} + \sqrt{b}} * \frac{\sqrt{a} - \sqrt{b}}{\sqrt{a} + \sqrt{b}}) * \frac{\sqrt{a}(\sqrt{a} + \sqrt{b})}{\sqrt{a} - \sqrt{b}} = (\frac{\sqrt{a} - \sqrt{b}}{\sqrt{a}(\sqrt{a} + \sqrt{b})} - \frac{\sqrt{a} - \sqrt{b}}{(\sqrt{a} + \sqrt{b})^2}) * \frac{\sqrt{a}(\sqrt{a} + \sqrt{b})}{\sqrt{a} - \sqrt{b}} = \frac{(\sqrt{a} - \sqrt{b})(\sqrt{a} + \sqrt{b}) - \sqrt{a}(\sqrt{a} - \sqrt{b})}{\sqrt{a}(\sqrt{a} + \sqrt{b})^2} * \frac{\sqrt{a}(\sqrt{a} + \sqrt{b})}{\sqrt{a} - \sqrt{b}} = \frac{(\sqrt{a} - \sqrt{b})(\sqrt{a} + \sqrt{b} - \sqrt{a})}{\sqrt{a} + \sqrt{b}} * \frac{1}{\sqrt{a} - \sqrt{b}} = \frac{\sqrt{b}}{\sqrt{a} + \sqrt{b}}$

$(\sqrt{a} + \sqrt{b} - \frac{2\sqrt{ab}}{\sqrt{a} + \sqrt{b}}) : (\frac{\sqrt{a} - \sqrt{b}}{\sqrt{a} + \sqrt{b}} + \frac{\sqrt{b}}{\sqrt{a}}) = \frac{\sqrt{a}(\sqrt{a} + \sqrt{b}) + \sqrt{b}(\sqrt{a} + \sqrt{b}) - 2\sqrt{ab}}{\sqrt{a} + \sqrt{b}} : \frac{\sqrt{a}(\sqrt{a} - \sqrt{b}) + \sqrt{b}(\sqrt{a} + \sqrt{b})}{\sqrt{a}(\sqrt{a} + \sqrt{b})} = \frac{a + \sqrt{ab} + \sqrt{ab} + b - 2\sqrt{ab}}{\sqrt{a} + \sqrt{b}} : \frac{a - \sqrt{ab} + \sqrt{ab} + b}{\sqrt{a}(\sqrt{a} + \sqrt{b})} = \frac{a + b}{\sqrt{a} + \sqrt{b}} : \frac{a + b}{\sqrt{a}(\sqrt{a} + \sqrt{b})} = \frac{a + b}{\sqrt{a} + \sqrt{b}} * \frac{\sqrt{a}(\sqrt{a} + \sqrt{b})}{a + b} = \sqrt{a}$