`***`Lời giải`***`
`P=(\frac{2}{\sqrt{x}}+\frac{\sqrt{x}}{\sqrt{x}+2}):\frac{2\sqrt{x}}{x+2\sqrt{x}}`
`=\frac{2(\sqrt{x}+2)+x}{\sqrt{x}(\sqrt{x}+2)}:\frac{2\sqrt{x}}{x+2\sqrt{x}}`
`=\frac{x+2\sqrt{x}+4}{\sqrt{x}(\sqrt{x}+2)}.\frac{\sqrt{x}(\sqrt{x}+2) }{2\sqrt{x}}`
`=\frac{x+2\sqrt{x}+4}{2\sqrt{x}}`
ĐKXĐ: `x>0`
Ta có: `P=3`
`=>\frac{x+2\sqrt{x}+4}{2\sqrt{x}}=3`
`<=>\frac{x+2\sqrt{x}+4}{2\sqrt{x}}-3=0`
`<=>\frac{x+2\sqrt{x}+4-3.2\sqrt{x}}{2\sqrt{x}}=0`
`<=>\frac{x+2\sqrt{x}+4-6\sqrt{x}}{2\sqrt{x}}=0`
`<=>\frac{x-4\sqrt{x}+4}{2\sqrt{x}}=0`
`<=>\frac{(\sqrt{x}-2)^2}{2\sqrt{x}}=0`
`=>(\sqrt{x}-2)^2=0`
`<=>\sqrt{x}-2=0`
`<=>\sqrt{x}=2`
`<=>x=4(N)`
Vậy `x=4` thì `P=3`
