Điều kiện: \(\left\{{}\begin{matrix}x\ge0\\x-\sqrt{x}\ne0\\x+2\sqrt{x}\ne0\\\left(\sqrt{x}-1\right)\left(x+2\sqrt{x}\right)\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>0\\x\ne1\end{matrix}\right.\)
\(C=\dfrac{x}{\sqrt{x}\left(\sqrt{x}-1\right)}+\dfrac{2}{\sqrt{x}\left(\sqrt{x}+2\right)}+\dfrac{x+2}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{x\left(\sqrt{x}+2\right)+2\left(\sqrt{x}-1\right)+\left(x+2\right)}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{\left(x\sqrt{x}+2x\right)+\left(2\sqrt{x}-2\right)+\left(x+2\right)}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{x\sqrt{x}+2x+2\sqrt{x}-2+x+2}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{\left(x\sqrt{x}+x\right)+\left(2x+2\sqrt{x}\right)}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{x\left(\sqrt{x}+1\right)+2\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{\left(x+2\sqrt{x}\right)\left(\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{\sqrt{x}\left(\sqrt{x}+2\right)\left(\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\)
