Đáp án + Giải thích các bước giải:
a)
`P=((\sqrtx)/(\sqrtx-1)-1/(\sqrtx+1)):(1/(\sqrtx+1)+2/(x-1))(x\ne1;x\ge0)`
`=>P=[(\sqrtx(\sqrtx+1))/(x-1)-(\sqrtx-1)/(x-1)]:((\sqrtx-1)/(x-1)+2/(x-1))`
`=>P=(x+\sqrtx-\sqrtx+1)/(x-1):(\sqrtx-1+2)/(x-1)`
`=>P=(x+1)/(x-1):(\sqrtx+1)/(x-1)`
`=>P=(x+1)/(x-1).(x-1)/(\sqrtx+1)`
`=>P=(x+1)/(\sqrtx+1)`
b)
Thay `x=4-2\sqrt3` vào `P` ta có:
`P=(4-2\sqrt3+1)/(\sqrt{4-2\sqrt3}+1)`
`=>P=(5-2\sqrt3)/(\sqrt{3-2\sqrt3+1}+1)`
`=>P=(5-2\sqrt3)/(\sqrt{(\sqrt3-1)^2}+1)`
`=>P=(5-2\sqrt3)/(|\sqrt3-1|+1)`
`=>P=(5-2\sqrt3)/(\sqrt3-1+1)`
`=>P=(5-2\sqrt3)/(\sqrt3)`
`=>P=(\sqrt3(5-2\sqrt3))/3`
`=>P=(5\sqrt3-6)/3`
