((1)/(\sqrt(x)-1)-(1)/(\sqrt(x)))(x-1) với x > 0 , x != 0 rút gọn biểu thức

$\\$ Với `x>0;x\ne1` ta có:

$\\$ `(1/(sqrtx-1)-1/sqrtx).(x-1)`

$\\$ `=[sqrtx/(sqrtx(sqrtx-1))-(sqrtx-1)/(sqrtx(sqrtx-1))].(x-1)`

$\\$ `=(sqrtx-sqrtx+1)/(sqrtx.(sqrtx-1)).((sqrtx-1)(sqrtx+1))`

$\\$ `=1/sqrtx .(sqrtx+1)`

$\\$ `=(sqrtx+1)/sqrtx`