Thực hiện phép tính `i) (xy)/((x^2 -y^2) - (x^2)/(y^2-x^2)` `k) 1/(3x - 2) - 1/(3x+2) - (3x-6)/(4-9x^2)` `l) y/(xy - 5x^2) - (15y - 25x)/(y^2 - 25x^2)`

Đáp án+Giải thích các bước giải:

 `i)`

`\frac{xy}{x^{2}-y^{2}}-\frac{x^{2}}{y^{2}-x^{2}}` `(đk:x\ney;x\ne-y)`

`=\frac{xy}{x^{2}-y^{2}}+\frac{x^{2}}{x^{2}-y^{2}}`

`=\frac{xy+x^{2}}{x^{2}-y^{2}}`

`=\frac{x.(x+y)}{(x-y).(x+y)}`

`=\frac{x}{x-y}`

`k)`

`\frac{1}{3x-2}-\frac{1}{3x+2}-\frac{3x-6}{4-9x^{2}}` `(đk:3x\ne2;3x\ne-2)`

`=\frac{3x+2}{(3x-2).(3x+2)}-\frac{3x-2}{(3x-2).(3x+2)}+\frac{3x-6}{(3x-2).(3x+2)}`

`=\frac{3x+2-3x+2+3x-6}{(3x-2).(3x+2)}`

`=\frac{3x-2}{(3x-2).(3x+2)}`

`=\frac{1}{3x+2}`

`l)`

`\frac{y}{xy-5x^{2}}-\frac{15y-25x}{y^{2}-25x^{2}}` `(đk:x\ne0;5x\ney;5x\ne-y;y\ne5x)`

`=\frac{y}{x.(y-5x)}-\frac{15y-25x}{y^{2}-(5x)^{2}}`

`=\frac{y}{x.(y-5x)}-\frac{15y-25x}{(y-5x).(y+5x)}`

`=\frac{y.(y+5x)}{x.(y-5x).(y+5x)}-\frac{x.(15y-25x)}{x.(y-5x).(y+5x)}`

`=\frac{y^{2}+5xy-15xy+25x^{2}}{x.(y-5x).(y+5x)}`

`=\frac{25x^{2}-10xy+y^{2}}{x.(y-5x).(y+5x)}`

`=\frac{y^{2}-2.y.5x+(5x)^{2}}{x.(y-5x).(y+5x)}`

`=\frac{(y-5x)^{2}}{x.(y-5x).(y+5x)}`

`=\frac{y-5x}{x.(y+5x)}`