Đáp án + Giải thích các bước giải:
+)ĐK: `x>=0,x\ne1`
`P=((x\sqrt{x}+x-2)/(x-1)-1/(\sqrt{x}+1)):1/(x\sqrt{x}-x)`
`=((x\sqrt{x}+x-2)/((\sqrt{x}-1)(\sqrt{x+1))-1/(\sqrt{x}+1)):1/(x(\sqrt{x}-1))`
`=((x\sqrt{x}+x-2-\sqrt{x}+1)/((\sqrt{x}-1)(\sqrt{x+1))).(x(\sqrt{x}-1))`
`=((x\sqrt{x}+x-\sqrt{x}-1)/((\sqrt{x}-1)(\sqrt{x+1))).(x(\sqrt{x}-1))`
`=((x(\sqrt{x}+1)-(\sqrt{x}+1))/((\sqrt{x}-1)(\sqrt{x+1))).(x(\sqrt{x}-1))`
`=(((\sqrt{x}+1)(x-1))/((\sqrt{x}-1)(\sqrt{x+1))).(x(\sqrt{x}-1))`
`=(x-1)/(\sqrt{x}-1).(x(\sqrt{x}-1))=(x-1)/(x)`
+) Ta có: `P=2`
`⇒(x-1)/(x)=2`
`⇒(x-1)/(x)-2=0`
`⇒x-1-2x=0
`⇒x=-1`
Vậy `x=-1` thì `P=2`
