Đáp án+Giải thích các bước giải:
`a)x/(x-2y)+x/(x+2y)+(4xy)/(4y^2-x^2)` (`ĐK: x\ne±2y`)
`=x/(x-2y)+x/(x+2y)-(4xy)/[(x-2y)(x+2y)]`
`=[x(x+2y)]/[(x-2y)(x+2y)]+[x(x-2y)]/[(x-2y)(x+2y)]-(4xy)/[(x-2y)(x+2y)]`
`=(x^2+2xy+x^2-2xy-4xy)/[(x-2y)(x+2y)]`
`=(2x^2-4xy)/[(x-2y)(x+2y)]`
`=[2x(x-2y)]/[(x-2y)(x+2y)]`
`=(2x)/(x+2y)`
`b)x^4/(1-x)+x^3+x^2+x+1` (`ĐK: x\ne1`)
`=x^4/(1-x)+[(x^3+x^2+x+1)(1-x)]/(1-x)`
`=(x^4+x^3+x^2+x+1-x^4-x^3-x^2-x)/(1-x)`
`=1/(1-x)`
