`((\sqrt{x} +2)/(x-1) - (\sqrt{x} -2)/(x-2\sqrt{x} + 1)) : ((4x)/(x-1)^2)` rút gọn

Đáp án:

Giải thích các bước giải:
ĐKXĐ : `x ne 1 ; x >= 0`

`( (sqrtx+2)/(x-1) - (sqrtx -2)/(x- 2sqrtx +1) ) :( 4x)/(x-1)^2`

`=[(sqrtx+2)/((sqrtx +1)(sqrtx -1)) - (sqrtx -2)/(sqrtx -1)^2 ]: (4x)/(x-1)^2`

`= [((sqrtx +2)(sqrtx -1))/((sqrtx +1)(sqrtx-1)^2) - ((sqrtx -2)(sqrtx+1))/((sqrtx +1)(sqrtx-1)^2)] : (4x)/(x-1)^2`

 `= [((sqrtx +2)(sqrtx -1) - (sqrtx -2)(sqrtx+1))/((sqrtx +1)(sqrtx-1)^2)] : (4x)/(x-1)^2`
`=( x + sqrtx -2 - x +sqrtx +2)/((sqrtx +1)(sqrtx-1)^2) . (x-1)^2/(4x)`

`= (2sqrtx)/((sqrtx +1)(sqrtx-1)^2) . [(sqrtx +1)(sqrtx-1)]^2/(4x)`

`= ( sqrtx +1)/(2sqrtx)` 
Vậy BT bằng ` ( sqrtx +1)/(2sqrtx)`  khi `x ne 1 ` và `x>=0`