a: Ta có: \(P=\left(\dfrac{x\sqrt{x}-1}{x-\sqrt{x}}-\dfrac{x\sqrt{x}+1}{x+\sqrt{x}}+\dfrac{x+1}{\sqrt{x}}\right):\left(\sqrt{x}-\dfrac{1}{\sqrt{x}}\right)\)
\(=\dfrac{x+\sqrt{x}+1-x+\sqrt{x}-1+x+1}{\sqrt{x}}:\dfrac{x-1}{\sqrt{x}}\)
\(=\dfrac{x+2\sqrt{x}+1}{\sqrt{x}}\cdot\dfrac{\sqrt{x}}{x-1}\)
\(=\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\)
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