\(\frac{a-b}{\sqrt{a}-\sqrt{b}}-\frac{\sqrt{a}^3-\sqrt{b}^3}{a+b+\sqrt{ab}}=\frac{\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)}{\sqrt{a}-\sqrt{b}}-\frac{\left(\sqrt{a}-\sqrt{b}\right)\left(a+\sqrt{ab}+b\right)}{a+b+\sqrt{ab}}\)
\(=\sqrt{a}+\sqrt{b}-\left(\sqrt{a}-\sqrt{b}\right)\)
\(=\sqrt{a}-\sqrt{a}+\sqrt{b}+\sqrt{b}=2\sqrt{b}\)