Đáp án:`a)P=(2\sqrtx)/(\sqrtx+1)`
`b)x=4+2\sqrt3<=>P=2\sqrt3-2`
`c)P<2`
Giải thích các bước giải:
`a)P=(\sqrtx+1)/(\sqrtx-1)+(\sqrtx-1)/(\sqrtx+1)-(2\sqrtx+2)/(x-1)(x>=0,x ne 1)`
`=(x+2\sqrtx+1+x-2\sqrtx+1-2\sqrtx-2)/(x-1)`
`=(2x-2\sqrtx)/(x-1)`
`=(2\sqrtx(\sqrtx-1))/((\sqrtx-1)(\sqrtx+1))`
`=(2\sqrtx)/(\sqrtx+1)`
`b)x=4+2\sqrt3=(\sqrt3+1)^2`
`=>P=(2(\sqrt3+1))/(\sqrt3+1+1)`
`=(2(\sqrt3+1))/(\sqrt3+2)`
`=(2(\sqrt3+1)(2-\sqrt3))/(4-3)`
`=2(2\sqrt3-3+2-\sqrt3)`
`=2(\sqrt3-1)`
`=2\sqrt3-2`
c)Xét `P-2`
`=(2\sqrtx-2\sqrtx-2)/(\sqrtx+1)`
`=-2/(\sqrtx+1)<0`
`=>P<2`
Vậy `P<2`
