作业帮化简:(x^2-1/x^2-2x+1+1-x/x+1)÷x/x-1
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/05 19:19:04
化简:(x^2-1/x^2-2x+1+1-x/x+1)÷x/x-1
化简:(x^2-1/x^2-2x+1+1-x/x+1)÷x/x-1
化简:(x^2-1/x^2-2x+1+1-x/x+1)÷x/x-1
=[(x+1)(x-1)/(x-1)²-(x-1)/(x+1)]×(x-1)/x
=[(x+1)/(x-1)-(x-1)/(x+1)]×(x-1)/x
=[(x+1)²-(x-1)²]/(x+1)(x-1)×(x-1)/x
=4x/(x+1)(x-1)×(x-1)/x
=4/(x+1)
解
原式
=[(x-1)(x+1)/(x-1)²+(1-x)/(x+1)]×(x-1)/x
=[(x+1)/(x-1)-(x-1)/(x+1)]×(x-1)/x
=(x+1)/x-(x-1)²/x(x+1)
=[(x+1)²-(x-1)²]/x(x+1)
=(2x+2x)/x(x+1)
=4/(x+1)