Đáp án+Giải thích các bước giải:
`P=\frac{15\sqrt{x}-11}{x+2\sqrt{x}-3}+\frac{3\sqrt{x}-2}{1-\sqrt{x}}-\frac{2\sqrt{x}+3}{\sqrt{x}+3}(x\ne9;x\ne1,x>=0)`
`=\frac{15\sqrt{x}-11}{x-\sqrt{x}+3\sqrt{x}-3}-\frac{3\sqrt{x}-2}{\sqrt{x}-1}-\frac{2\sqrt{x}+3}{\sqrt{x}+3}`
`=\frac{15\sqrt{x}-11}{(\sqrt{x}-1)(\sqrt{x}+3)}-\frac{3\sqrt{x}-2}{\sqrt{x}-1}-\frac{2\sqrt{x}+3}{\sqrt{x}+3}`
`=\frac{15\sqrt{x}-11}{(\sqrt{x}-1)(\sqrt{x}+3)}-\frac{(3\sqrt{x}-2)(\sqrt{x}+3)}{(\sqrt{x}-1)(\sqrt{x}+3)}-\frac{(2\sqrt{x}+3)(\sqrt{x}-1)}{(\sqrt{x}-1)(\sqrt{x}+3)}`
`=\frac{15\sqrt{x}-11-(3x+9\sqrt{x}-2\sqrt{x}-9)-(2x-2\sqrt{x}+3\sqrt{x}-3)}{{(\sqrt{x}-1)(\sqrt{x}+3)}`
`=\frac{15\sqrt{x}-11-(3x+7\sqrt{x}-6)-(2x+\sqrt{x}-3)}{{(\sqrt{x}-1)(\sqrt{x}+3)}`
`=\frac{15\sqrt{x}-11-3x-7\sqrt{x}+6-2x-\sqrt{x}+3}{(\sqrt{x}-1)(\sqrt{x}+3)}`
`=\frac{-5x+7\sqrt{x}-2}{(\sqrt{x}-1)(\sqrt{x}+3)}`
`=\frac{-5x+5\sqrt{x}+2\sqrt{x}-2}{(\sqrt{x}-1)(\sqrt{x}+3)}`
`=\frac{(\sqrt{x}-1)(-5\sqrt{x}+2)}{(\sqrt{x}-1)(\sqrt{x}+3)}`
`=\frac{-5\sqrt{x}+2}{\sqrt{x}+3}`
`b)P=1/2`
`<=>\frac{-5\sqrt{x}+2}{\sqrt{x}+3}=1/2`
`<=>2(-5\sqrt{x}+2)=\sqrt{x}+3`
`<=>-10\sqrt{x}+4=\sqrt{x}+3`
`<=>11\sqrt{x}=1`
`<=>\sqrt{x}=1/11`
`<=>x=1/121`
Vậy `x=1/121` thì `P=1/2`
`c)P=\frac{-5\sqrt{x}+2}{\sqrt{x}+3}`
`=\frac{-5\sqrt{x}-15+17}{\sqrt{x}+3}`
`=\frac{-5(\sqrt{x}+3)+17}{\sqrt{x}+3}`
`=-5+\frac{17}{\sqrt{x}+3}`
Ta có `\sqrt{x}+3>=3`
`<=>\frac{17}{\sqrt{x}+3}<=17/3`
`->-5+\frac{17}{\sqrt{x}+3}<=-5+17/3=2/3`
`->P<=2/3`(đpcm)
