Điều kiện: \(\left\{{}\begin{matrix}x\ge0\\x-\sqrt{x}\ne0\\x+2\sqrt{x}\ne0\\\left(\sqrt{x}+1\right)\left(x+2\sqrt{x}\right)\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>0\\x\ne1\end{matrix}\right.\)
\(C=\dfrac{x}{\sqrt{x}\left(\sqrt{x}-1\right)}+\dfrac{2}{\sqrt{x}\left(\sqrt{x}+2\right)}+\dfrac{x+2}{\sqrt{x}\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{x\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)+2\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)+\left(\sqrt{x}-1\right)\left(x+2\right)}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{x\left(x+3\sqrt{x}+2\right)+2\left(x-1\right)+\left(x\sqrt{x}+2\sqrt{x}-x-2\right)}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{\left(x^2+3x\sqrt{x}+2x\right)+\left(2x-2\right)+\left(x\sqrt{x}+2\sqrt{x}-x-2\right)}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{x^2+3x\sqrt{x}+2x+2x-2+x\sqrt{x}+2\sqrt{x}-x-2}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{\left(x^2+3x-4\right)+\left(2\sqrt{x}+4x\sqrt{x}\right)}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)}\)
