Đáp án:
Giải thích các bước giải:
`{2x}/{x^2+2xy} - {y}/{2y^2-xy} + 4/{x^2 - 4y^2}`
`={2x}/{x(x+2y)} - {-y}/{y(x-2y)} + 4/{(x+2y)(x-2y)}` `(1)`
ĐKXĐ: `x\ne0, x\ne-2y, x\ne2y`
Khi đó `(1) <=>{2x.y(x-2y)}/{x(x+2y)y(x-2y)} + {xy(x+2y)}/{xy(x-2y)(x+2y)} + {4xy}/{xy(x+2y)(x-2y)}`
`={2x^2y-4xy^2}/{x(x+2y)y(x-2y)} + {x^2y+2xy^2}/{xy(x-2y)(x+2y)} + {4xy}/{xy(x+2y)(x-2y)}`
`={2x^2y-4xy^2 + x^2y+2xy^2+4xy }/{x(x+2y)y(x-2y}`
`={3x^2y−2xy^2+4xy}/{x(x+2y)y(x-2y)}`
`={xy(3x - 2y + 4)}/{xy(x+2y)(x-2y)}`
`={3x - 2y + 4}/{(x+2y)(x-2y)}.`
