`a,`

`A = 1 -1/(\sqrt{x})`         đk `x>0`

`x =4(tm)`

`\sqrt{x} =2`

Với `x=4` ta có :

`A = 1 -1/2 = 1/2`

Vậy `A=1/2` khi `x=4`

`b,`

`B = (\sqrt{x})/(\sqrt{x} +3) -1/(\sqrt{x} -1) +3/((\sqrt{x} -1)(\sqrt{x} +3))`           đk `x >0 , x \ne 1`

`B = (\sqrt{x}(\sqrt{x} -1))/((\sqrt{x} +3)(\sqrt{x} -1)) -(\sqrt{x} +3)/((\sqrt{x} -1)(\sqrt{x} +3)) +3/((\sqrt{x} -1)(\sqrt{x} +3))`

`B = (\sqrt{x}(\sqrt{x} -1)-\sqrt{x} -3+3)/((\sqrt{x} -1)(\sqrt{x} +3))`

`B = (x -\sqrt{x}-\sqrt{x} -3+3)/((\sqrt{x} -1)(\sqrt{x} +3))`

`B = (x -2\sqrt{x})/((\sqrt{x} -1)(\sqrt{x} +3))`

`P = B*A`

`=> P = (x -2\sqrt{x})/((\sqrt{x} -1)(\sqrt{x} +3)) * (1 -1/(\sqrt{x}))`

`=> P = (\sqrt{x}(\sqrt{x} -2))/((\sqrt{x} -1)(\sqrt{x} +3)) * ( \sqrt{x}-1)/(\sqrt{x})`

`=> P = (\sqrt{x} -2)/(\sqrt{x} +3)`

Vậy `P = (\sqrt{x} -2)/(\sqrt{x} +3)` với `x >0 , x \ne 1`

`c,`

`P = (\sqrt{x} -2)/(\sqrt{x} +3)`

`P = 1 - 5/(\sqrt{x} +3)`

Ta có : `\sqrt{x} ≥0`

`=> \sqrt{x} +3≥3`

`=> 0 < 1/(\sqrt{x} +3) ≤ 1/3`

`=> 0> -5/(\sqrt{x} +3) ≥ -5/3`

`=> 1 > 1 -5/(\sqrt{x} +3) ≥ -2/3`

`=> 1 > P ≥-2/3`

`=> 1 -5/(\sqrt{x} +3) ∈{0}`

`=> -5/(\sqrt{x} +3) ∈{-1}`

`=> \sqrt{x} +3 ∈{5}`

`=> \sqrt{x}∈{2}`

`=> x=4` kết hợp điều kiện

Vậy `x=4` thì P nguyên