Đáp án:
`A = 5/(x + y)`
Giải thích các bước giải:
`A = (2x)/(x^2 + xy) + (6x)/(x^2 - y^2) + 3/(y - x)`
` = (2x)/[x(x + y)] + (6x)/[(x + y)(x - y)] + (-3)/(x - y)`
`= [2x(x - y)]/[x(x + y)(x - y)] + (6x.x)/[x(x + y)(x - y)] + [(-3).x(x + y)]/[x(x + y)(x - y)]`
`= [2x(x - y) + 6x^2 + (-3x)(x + y)]/[x(x + y)(x - y)] = [2x^2 - 2xy + 6x^2 + (-3x^2 - 3xy)]/[x(x + y)(x - y)]`
`= [2x^2 - 2xy + 6x^2 - 3x^2 - 3xy]/[x(x + y)(x - y)] = [5x^2 - 5xy]/[x(x + y)(x - y)] = [5x(x - y)]/[x(x + y)(x - y)] = 5/(x + y)`
