Ta có: \(C=\frac{a\sqrt{a}-1}{a-\sqrt{a}}+\frac{\sqrt{a}-1}{\sqrt{a}}\left(\frac{\sqrt{a}+1}{\sqrt{a}-1}+\frac{\sqrt{a}-1}{\sqrt{a}+1}\right)\)
\(=\frac{\left(\sqrt{a}-1\right)\left(a+\sqrt{a}+1\right)}{\sqrt{a}\left(\sqrt{a}-1\right)}+\frac{\sqrt{a}-1}{\sqrt{a}}\cdot\left(\frac{\left(\sqrt{a}+1\right)^2+\left(\sqrt{a}-1\right)^2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\right)\)
\(=\frac{a+\sqrt{a}+1}{\sqrt{a}}+\frac{\sqrt{a}-1}{\sqrt{a}}\cdot\frac{2a+2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\)
\(=\frac{2\left(a+1\right)}{\sqrt{a}\cdot\left(\sqrt{a}+1\right)}+\frac{a+\sqrt{a}+1}{\sqrt{a}}\)
\(=\frac{2\left(a+1\right)}{\sqrt{a}\cdot\left(\sqrt{a}+1\right)}+\frac{\left(\sqrt{a}+1\right)\left(a+\sqrt{a}+1\right)}{\sqrt{a}\left(\sqrt{a}+1\right)}\)
\(=\frac{2a+2+a\sqrt{a}+2a+2\sqrt{a}+1}{\sqrt{a}\cdot\left(\sqrt{a}+1\right)}\)
\(=\frac{a\sqrt{a}+4a+2\sqrt{a}+3}{\sqrt{a}\cdot\left(\sqrt{a}+1\right)}\)