Đáp án+Giải thích các bước giải:

b) Ta có:

`P = A + B  (x > 0)`

`= (x - 6)/(x + 3 sqrtx) - 1/(sqrtx)`

`= (x - 6)/(sqrtx (sqrtx + 3)) - (sqrtx + 3)/(sqrtx (sqrtx + 3)) + (sqrtx)/(sqrtx(sqrtx + 3))`

`= (x - 6 - sqrtx - 3 + sqrtx)/(sqrtx (sqrtx + 3))`

`= (x - 9)/(sqrtx (sqrtx + 3))`

`= ((sqrtx-3)(sqrtx+3))/(sqrtx(sqrtx+3))`

`= (sqrtx-3)/(sqrtx)`

Vậy `P = (sqrtx - 3)/(sqrtx)` với `x > 0` (đpcm)

c) `P = (sqrtx - 3)/(sqrtx)`

`= 1 - 3/(sqrtx)`

`P` nguyên khi `3/(sqrtx)` nguyên

`-> 3 vdots sqrtx`

`-> sqrtx in Ư(3) = {-3;-1;1;3}`

mà `sqrtx >= 0` nên `sqrtx in {1;3} => x in {1;9}` (tm)

Vậy `x in {1;9}` thì `P` nguyên

`\ttcolor{red}{#ILy}`