giúp mk bài này vs ạ

`a)`

`A=((2xy)/(x^2 -y^2) + (x-y)/(2x+2y)) . (2x)/(x+y) + (y)/(y-x) + (2-x)/(x-y)`  `ĐKXĐ: x^2 \ne y^2`

`=(4xy+(x-y)^2)/(2(x+y)(x-y)) . (2x)/(x+y) + (-y+2-x)/(x-y)`

`=(2x(4xy +x^2 -2xy+y^2))/(2(x+y)^2 (x-y)) + (2-x-y)/(x-y)`

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

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

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

Với `x=3;y=1 => A=(2-1)/(3-1) = 1/2`

`b)`

`A . (x^3 -y^3)/(2-y)`

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

`= x^2 +xy+y^2`

Ta có:

`(x+y)^2 >= 0`

`=> x^2 + y^2 >= -2xy`

`=> x^2 +y^2 >= - xy`

`=> x^2 + xy + y^2 >=0`

`=> A . (x^3 - y^3)/(2-y) >= 0`.