a: \(\frac{a-b}{\sqrt{a}-\sqrt{b}}-\frac{\sqrt{a^3}+\sqrt{b^3}}{a-b}\)
\(=\frac{\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}{\sqrt{a}-\sqrt{b}}-\frac{\left(\sqrt{a}+\sqrt{b}\right)\left(a-\sqrt{ab}+b\right)}{\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}\)
\(=\left(\sqrt{a}+\sqrt{b}\right)-\frac{a-\sqrt{ab}+b}{\sqrt{a}-\sqrt{b}}=\frac{\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)-a+\sqrt{ab}-b}{\sqrt{a}-\sqrt{b}}\)
\(=\frac{a-b-a+\sqrt{ab}-b}{\sqrt{a}-\sqrt{b}}=\frac{\sqrt{ab}-2b}{\sqrt{a}-\sqrt{b}}\)
b: \(\frac{2a+\sqrt{ab}-3b}{2a-5\sqrt{ab}+3b}\)
\(=\frac{2a+3\sqrt{ab}-2\sqrt{ab}-3b}{2a-2\sqrt{ab}-3\sqrt{ab}+3b}=\frac{\sqrt{a}\left(2\sqrt{a}+3\sqrt{b}\right)-\sqrt{b}\left(2\sqrt{a}+\sqrt{b}\right)}{2\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)-3\sqrt{b}\left(\sqrt{a}-\sqrt{b}\right)}\)
\(=\frac{\left(2\sqrt{a}+3\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}{\left(2\sqrt{a}-3\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}=\frac{2\sqrt{a}+3\sqrt{b}}{2\sqrt{a}-3\sqrt{b}}\)
