b: \(\frac{\left(2+\sqrt{a}\right)^2-\left(\sqrt{a}-3\right)^2}{2a-\sqrt{a}}\)
\(=\frac{a+4\sqrt{a}+4-a+6\sqrt{a}-9}{\sqrt{a}\left(2\sqrt{a}-1\right)}\)
\(=\frac{10\sqrt{a}-5}{\sqrt{a}\left(2\sqrt{a}-1\right)}=\frac{5\left(2\sqrt{a}-1\right)}{\sqrt{a}\left(2\sqrt{a}-1\right)}=\frac{5}{\sqrt{a}}\)
d: \(\left(2-\frac{a-3\sqrt{a}}{\sqrt{a}-3}\right)\left(2-\frac{5\sqrt{a}-\sqrt{ab}}{\sqrt{b}-5}\right)\)
\(=\left(2-\frac{\sqrt{a}\left(\sqrt{a}-3\right)}{\sqrt{a}-3}\right)\left(2+\frac{\sqrt{a}\left(\sqrt{b}-5\right)}{\sqrt{b}-5}\right)\)
\(=\left(2-\sqrt{a}\right)\left(2+\sqrt{a}\right)=4-a\)
b: \(\frac{a+b-2\sqrt{ab}}{\sqrt{a}-\sqrt{b}}-\frac{a-b}{\sqrt{a}+\sqrt{b}}\)
\(=\frac{\left(\sqrt{a}-\sqrt{b}\right)^2}{\sqrt{a}-\sqrt{b}}-\frac{\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)}{\left(\sqrt{a}+\sqrt{b}\right)}\)
\(=\sqrt{a}-\sqrt{b}-\left(\sqrt{a}-\sqrt{b}\right)\)
=0
d: \(\left(\frac{a\cdot\sqrt{a}+b\cdot\sqrt{b}}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\right)\cdot\frac{\sqrt{a}+\sqrt{b}}{a-b}\)
\(=\left(\frac{\left(\sqrt{a}+\sqrt{b}\right)\left(a-\sqrt{ab}+b\right)}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\right)\cdot\frac{1}{\sqrt{a}-\sqrt{b}}\)
\(=\frac{\left(a-\sqrt{ab}+b-\sqrt{ab}\right)}{\sqrt{a}-\sqrt{b}}=\frac{\left(\sqrt{a}-\sqrt{b}\right)^2}{\left(\sqrt{a}-\sqrt{b}\right)}=\sqrt{a}-\sqrt{b}\)
