`ĐK:{(x ge 0),(x ne 4),(x ne 9):}`
`P=(2\sqrt{x}-9)/(x-5\sqrt{x}+6)-(\sqrt{x}+3)/(\sqrt{x}-2)-(2\sqrt{x}+1)/(3-\sqrt{x)}`
`=(2\sqrt{x}-9)/((\sqrt{x}-2)(\sqrt{x}-3))-(\sqrt{x}+3)/(\sqrt{x}-2)+(2\sqrt{x}+1)/(\sqrt{x}-3)`
`=(2\sqrt{x}-9-(\sqrt{x}+3)(\sqrt{x}-3)+(2\sqrt{x}+1)(\sqrt{x}-2))/((\sqrt{x}-2)(\sqrt{x}-3))`
`=(2\sqrt{x}-9-x+9+2x-3\sqrt{x}-2)/((\sqrt{x}-2)(\sqrt{x}-3))`
`=(-\sqrt{x}+x-2)/((\sqrt{x}-2)(\sqrt{x}-3))`
`=-(x-\sqrt{x}+2)/((\sqrt{x}-2)(\sqrt{x}-3))`
`=((\sqrt{x}+1)(\sqrt{x}-2))/((\sqrt{x}-2)(\sqrt{x}-3))`
`=(\sqrt{x}+1)/(\sqrt{x}-3)`
a)tìm x để p=2
`->(\sqrt{x}+1)/(\sqrt{x}-3)=2`
`↔\sqrt{x}+1=2(\sqrt{x}-3)`
`↔\sqrt{x}+1=2\sqrt{x}-6`
`↔-\sqrt{x}=-7`
`↔\sqrt{x}=7`
`↔x=49`
Vậy `x=49` thì `P=2`
b)tìm p để x=0
`->P=(\sqrt{0}+1)/(\sqrt{0}-3)`
`↔P=(0+1)/(0-3)`
`↔P=-1/3`
Vậy `P=-1/3` thì `x=0`
c)tìm x thuộc z để p nhận giá trị nguyên
`(\sqrt{x}+1)/(\sqrt{x}-3)`
`=(\sqrt{x}-3+4)/(\sqrt{x}-3)`
`=1+4/(\sqrt{x}-3)`
`->\sqrt{x}-3∈Ư(4)`
`↔`\(\left[ \begin{array}{l}\sqrt{x}-3=-4\\\sqrt{x}-3=-2\\\sqrt{x}-3=-1\\\sqrt{x}-3=1\\\sqrt{x}-3=2\\\sqrt{x}-3=4\end{array} \right.\)
`↔`\(\left[ \begin{array}{l}\sqrt{x}=-1(KTM)\\\sqrt{x}=1\\\sqrt{x}=2\\\sqrt{x}=4(KTM)\\\sqrt{x}=5\\\sqrt{x}=7\end{array} \right.\)
Vậy `x={1;2;5;7}` thì `P` nguyên
