Đáp án:
`(1/(x-\sqrtx)+1/(\sqrtx-1)):(\sqrtx+1)/(\sqrtx-1)^2=(\sqrtx-1)/\sqrtx`
Giải thích các bước giải:
Với `x>0;x\ne1`
`(1/(x-\sqrtx)+1/(\sqrtx-1)):(\sqrtx+1)/(\sqrtx-1)^2`
`=(1/(\sqrtx(\sqrtx-1))+1/(\sqrtx-1)):(\sqrtx+1)/(\sqrtx-1)^2`
`=(1+\sqrtx)/(\sqrtx(\sqrtx-1)):(\sqrtx+1)/(\sqrtx-1)^2`
`=(1+\sqrtx)/(\sqrtx(\sqrtx-1)).(\sqrtx-1)^2/(\sqrtx+1)`
`=(\sqrtx-1)^2/(\sqrtx(\sqrtx-1))`
`=(\sqrtx-1)/\sqrtx`
Vậy `x>0;x\ne1` thì `(1/(x-\sqrtx)+1/(\sqrtx-1)):(\sqrtx+1)/(\sqrtx-1)^2=(\sqrtx-1)/\sqrtx`
