( 1/ căn x -1 + căn x / x-1 ): 2 căn x +1 / x+căn x -2

`(1/(sqrtx - 1) + (sqrtx)/(x - 1)) : (2sqrtx + 1)/(x + sqrtx - 2) (x >= 0 ; x\ne 1)`

`= [(sqrtx + 1)/((sqrtx - 1)(sqrtx + 1)) + (sqrtx)/((sqrtx - 1)(sqrtx + 1))] . (x + sqrtx - 2)/(2sqrtx + 1)`

`= (sqrtx + 1 + sqrtx)/((sqrtx- 1)(sqrtx + 1)) . ((sqrtx - 1)(sqrtx + 2))/(2sqrtx + 1)`

`= (2sqrtx + 1)/((sqrtx - 1)(sqrtx + 1)) . ((sqrtx - 1)(sqrtx + 2))/(2sqrtx + 1)`

`= (sqrtx + 2)/(sqrtx + 1)`

Vậy với `x >= 0 ; x\ne 1` thì biểu thức bằng `(sqrtx + 2)/(sqrtx + 1)`