1: \(\left(\sqrt{ab}+2\cdot\sqrt{\frac{b}{a}}-\sqrt{\frac{a}{b}}+\sqrt{\frac{1}{ab}}\right)\cdot\sqrt{ab}\)
\(=\sqrt{ab\cdot ab}+2\cdot\sqrt{\frac{b}{a}\cdot ab}-\sqrt{\frac{a}{b}\cdot ab}+1\)
\(=ab+2\sqrt{b^2}-\sqrt{a^2}+1=ab+2b-a+1\)
3: \(\frac{a-\sqrt{ab}+b}{a\cdot\sqrt{a}+b\cdot\sqrt{b}}-\frac{\sqrt{a}-\sqrt{b}-1}{a-b}\)
\(=\frac{1}{\sqrt{a}+\sqrt{b}}-\frac{\sqrt{a}-\sqrt{b}-1}{a-b}\)
\(=\frac{\sqrt{a}-\sqrt{b}-\sqrt{a}+\sqrt{b}+1}{a-b}=\frac{1}{a-b}\)
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