cộng phân thức nhé cảm ơn nhiều

Đáp án:

 `d)`

`\frac{1}{x-2}+\frac{2}{x+2}+\frac{x}{x^{2}-4}` `(đk: x\ne\pm2)`

`=\frac{1.(x+2)}{x^{2}-4}+\frac{2.(x-2)}{x^{2}-4}+\frac{x}{x^{2}-4}`

`=\frac{x+2+2x-4+x}{x^{2}-4}`

`=\frac{(x+2x+x)+(2-4)}{x^{2}-4}`

`=\frac{4x-2}{x^{2}-4}`

`e)`

`\frac{x+1}{2x-2}+\frac{x^{2}+3}{2-2x^{2}}` `(x\ne\pm1)`

`=\frac{x+1}{2.(x-1)}+\frac{x^{2}+3}}{2.(1-x^{2})}`

`=\frac{(x+1)^{2}}{2.(x^{2}-1)}-\frac{x^{2}+3}{2.(x^{2}-1)}`

`=\frac{x^{2}+2x+1-x^{2}-3}{2.(x^{2}-1)}`

`=\frac{(x^{2}-x^{2})+2x-2}{2.(x^{2}-1)}`

`=\frac{2.(x-1)}{2.(x-1).(x+1)}`

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

`g)`

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

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

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

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

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

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

`#DYNA`