`a)`

`A = sqrt(x) / (sqrt(x) + 2)`

Thay `x = 4` (tmdk) vào `A` ta được:

`A = sqrt(4) / (sqrt(4) + 2)`

`A = 2/(2 + 2)`

`A = 2/4`

`A = 1/2`

`b)`

`B = 2 / (sqrt(x) - 1) - (sqrt(x) - 2)/(x - sqrt(x))`

`= 2/(sqrt(x) - 1) - (sqrt(x) - 2)/(sqrt(x)(sqrt(x) - 1))`

`= (2sqrt(x)) / (sqrt(x)(sqrt(x) - 1)) - (sqrt(x) - 2)/(sqrt(x)(sqrt(x) - 1))`

`= (2sqrt(x) - (sqrt(x) - 2))/(x - sqrt(x))`

`= (2sqrt(x) - sqrt(x) + 2)/(x - sqrt(x))`

`= (sqrt(x) + 2)/(x - sqrt(x))` (đpcm)

`c)`

`P = sqrt(x)/(sqrt(x) + 2) + 1/((sqrt(x) + 2)/(x - sqrt(x)))`

`P = sqrt(x)/(sqrt(x) + 2) + (x - sqrt(x))/(sqrt(x) + 2)`

`P = (sqrt(x) + x - sqrt(x))/(sqrt(x) + 2)`

`P = x/(sqrt(x) + 2)`

Để `P >= 1:`

`x/(sqrt(x) + 2) >= 1`

`=> x >= sqrt(x) + 2`

`=> x - sqrt(x) - 2 >= 0`

`=> (sqrt(x) - 2)(sqrt(x) + 1) >= 0`

Vì `sqrt(x) + 1 > 0` nên `sqrt(x) - 2 >= 0`

`=> sqrt(x) >= 2`

`=> x >= 4` (thỏa mãn điều kiện)

Vậy `x >= 4` thì `P >= 1`

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