Đáp án`+`Giải thích các bước giải:

 `1)`Tại `x=9` thì :

`B = (2*sqrt9 + 1)/(9 + sqrt9 -2) = (6+1)/(9+3-2) = 7/10`

Vậy `B= 7/10` khi `x=9`

`2)`

`M = A: B (ĐKXĐ: x >= 0; x ne 1)`

`= (1/(sqrtx -1) + (sqrtx)/(x-1)) : (2sqrtx +1)/(x + sqrtx-2)`

`= (1/(sqrtx -1) + (sqrtx)/((sqrtx -1)(sqrtx +1))) * (x + 2sqrtx - sqrtx-2)/(2sqrtx +1)`

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

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

Vậy `M = (sqrtx+2)/(sqrtx+1)`

`3)`

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

Có: `sqrtx >= 0 -> sqrtx + 1 >= 1 -> 1/(sqrtx +1) <= 1 AA x`

`-> M = 1 + 1/(sqrt +1) <= 1 + 1 = 2`

Dấu "=" xảy ra khi `sqrtx = 0 <=> x=0`

Vậy `max M = 2 <=> x=0`