giải giúp ạ toán lớp 9 ạ

`a)` Điều kiện: `x > 0, y > 0, x ne y`

`P = [sqrt(x) + (y - sqrt(xy)) / (sqrt(x) + sqrt(y))] : [x / (sqrt(xy) + y) + y / (sqrt(xy) - x) - (x + y) / sqrt(xy)]`

Ta có:

`sqrt(x) + (y - sqrt(xy)) / (sqrt(x) + sqrt(y))`

`= (sqrt(x)(sqrt(x) + sqrt(y)) + y - sqrt(xy)) / (sqrt(x) + sqrt(y))`

`= (x + sqrt(xy) + y - sqrt(xy)) / (sqrt(x) + sqrt(y))`

`= (x + y) / (sqrt(x) + sqrt(y))`

Lại có:

`x / (sqrt(xy) + y) + y / (sqrt(xy) - x) - (x + y) / sqrt(xy)`

`= x / (sqrt(y)(sqrt(x) + sqrt(y))) - y / (sqrt(x)(sqrt(x) - sqrt(y))) - (x + y) / sqrt(xy)`

`= (xsqrt(x)(sqrt(x) - sqrt(y)) - ysqrt(y)(sqrt(x) + sqrt(y)) - (x + y)(x - y)) / (sqrt(xy)(x - y))`

`= (x^2 - xsqrt(xy) - ysqrt(xy) - y^2 - (x^2 - y^2)) / (sqrt(xy)(x - y))`

`= (x^2 - y^2 - sqrt(xy)(x + y) - x^2 + y^2) / (sqrt(xy)(x - y))`

`= (-sqrt(xy)(x + y)) / (sqrt(xy)(x - y))`

`= -(x + y) / (x - y) = (x + y) / (y - x)`

Suy ra:

`P = (x + y) / (sqrt(x) + sqrt(y)) : (x + y) / (y - x)`

`P = (x + y) / (sqrt(x) + sqrt(y)) * (y - x) / (x + y)`

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

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

`P = sqrt(y) - sqrt(x)`

`b)` Với `x = 3`, `y = 4 + 2sqrt(3)` ta có:

`y = 3 + 2sqrt(3) + 1 = (sqrt(3) + 1)^2`

`=> sqrt(y) = sqrt((sqrt(3) + 1)^2) = sqrt(3) + 1`

`sqrt(x) = sqrt(3)`

Thay vào `P`, ta được:

`P = (sqrt(3) + 1) - sqrt(3) = 1`