a) Ta có: \(C=\left(\frac{1}{\sqrt{a}-1}+\frac{1}{\sqrt{a}}\right):\frac{\sqrt{a}+1}{\sqrt{a}-2}-\frac{\sqrt{a}+2}{\sqrt{a}-4}\)
\(=\left(\frac{\sqrt{a}}{\sqrt{a}\left(\sqrt{a}-1\right)}+\frac{\sqrt{a}-1}{\sqrt{a}\left(\sqrt{a}-1\right)}\right)\cdot\frac{\sqrt{a}-2}{\sqrt{a}+1}-\frac{\sqrt{a}+2}{\sqrt{a}-4}\)
\(=\frac{2\sqrt{a}}{\sqrt{a}\left(\sqrt{a}-1\right)}\cdot\frac{\sqrt{a}-2}{\sqrt{a}+1}-\frac{\sqrt{a}+2}{\sqrt{a}-4}\)
\(=\frac{2\left(\sqrt{a}-2\right)}{a-1}-\frac{\sqrt{a}+2}{\sqrt{a}-4}\)
\(=\frac{2\left(a-6\sqrt{a}+8\right)-\left(\sqrt{a}+2\right)\left(a-1\right)}{\left(a-1\right)\left(\sqrt{a}-4\right)}\)
\(=\frac{2a-12\sqrt{a}+18-\left(a\sqrt{a}-\sqrt{a}+2a-2\right)}{\left(a-1\right)\left(\sqrt{a}-4\right)}\)
\(=\frac{2a-12\sqrt{a}+18-a\sqrt{a}+\sqrt{a}-2a+2}{\left(a-1\right)\left(\sqrt{a}-4\right)}\)
\(=\frac{-11\sqrt{a}+20-a\sqrt{a}}{\left(a-1\right)\left(\sqrt{a}-4\right)}\)
