`a)ĐKXĐ: x >0; x \ne 1`
`P=\frac{x\sqrt{x}-1}{x-\sqrt{x}}-\frac{x\sqrt{x}+1}{x+\sqrt{x}}+\frac{x+1}{\sqrt{x}}(x >0)`
`=\frac{x\sqrt{x}-1}{\sqrt{x}(\sqrt{x}-1)}-\frac{x\sqrt{x}+1}{\sqrt{x}(\sqrt{x}+1)}+\frac{x+1}{\sqrt{x}}`
`=\frac{(x\sqrt{x}-1)(\sqrt{x}+1)-(x\sqrt{x}+1)(\sqrt{x}-1)+(x+1)(x-1)}{\sqrt{x}(\sqrt{x}+1)(\sqrt{x}-1)}`
`=\frac{x^2+x\sqrt{x}-\sqrt{x}-1-(x^2-x\sqrt{x}+\sqrt{x}-1)+x^2-1}{\sqrt{x}(\sqrt{x}+1)(\sqrt{x}-1)}`
`=\frac{x^2+x\sqrt{x}-1\sqrt{x}-1-x^2+x\sqrt{x}-\sqrt{x}+1+x^2-1}{\sqrt{x}(\sqrt{x}+1)(\sqrt{x}-1)}`
`=\frac{x^2+2x\sqrt{x}-2\sqrt{x}-2}{\sqrt{x}(\sqrt{x}+1)(\sqrt{x}-1)}`
`=\frac{2\sqrt{x}+x+1}{\sqrt{x}}`
`b)P=\frac{9}{2}`
`<=>\frac{2\sqrt{x}+x+1}{\sqrt{x}}=\frac{9}{2}`
`<=>4\sqrt{x}+2x+2-9\sqrt{x}=0`
`<=>2x-5\sqrt{x}+2=0`
`<=>2x-5\sqrt{x}+2=0`
`<=>`\(\left[ \begin{array}{l}\sqrt{x}=2\\\sqrt{x}=\dfrac{1}{2}\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=4\\x=\dfrac{1}{4}\end{array} \right.\)
