Ta có: \(P=\frac{\sqrt{x}+1}{x-1}-\frac{x+2}{x\sqrt{x}-1}-\frac{\sqrt{x}+1}{x+\sqrt{x}+1}\) \(Đkxđ:\left\{{}\begin{matrix}x\ne1\\x>0\end{matrix}\right.\)
\(P=\frac{\left(\sqrt{x}+1\right)\left(x+\sqrt{x}+1\right)-x-2-\left(\sqrt{x}+1\right)\left(x-1\right)}{\left(x-1\right)\left(x+\sqrt{x}+1\right)}\)
\(P=\frac{x\sqrt{x}+x+\sqrt{x}+x+\sqrt{x}+1-x-2-x\sqrt{x}+\sqrt{x}-x+1}{\left(x+\sqrt{x}+1\right)\left(x-1\right)}\)
\(P=\frac{3\sqrt{x}}{\left(x-1\right)\left(x+\sqrt{x}+1\right)}\)
\(P=\frac{3\sqrt{x}}{x\sqrt{x}-1}\)
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