Ta có:
$\dfrac{a\sqrt{a} + b\sqrt{b}}{\sqrt{a} + \sqrt{b}} - \sqrt{ab} = \dfrac{(\sqrt{a})^3 + (\sqrt{b})^3}{\sqrt{a} + \sqrt{b}} = \dfrac{(\sqrt{a} + \sqrt{b})(a - \sqrt{ab} + b)}{\sqrt{a} + \sqrt{b}} - \sqrt{ab} =$
$a - \sqrt{ab} + b - \sqrt{ab} = a - 2\sqrt{ab} + b = (\sqrt{a} - \sqrt{b})^2$