Question

化简[(x^2-1)/(x^2-2x+1)+(1-x)/(x+1)]÷x/(x-1)要具体工程

Answer 1

原式=[(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)-(x-1)]/[(x+1)(x-1)]×(x-1)/x
=2/[(x+1)(x-1)]×(x-1)/x
=2/[x(x+1)]

很高兴为您解答，祝你学习进步！【学习宝典】团队为您答题。
有不明白的可以追问！如果您认可我的回答。
请点击下面的【选为满意回答】按钮。
如果有其他问题请另发或点击向我求助，答题不易，请谅解，谢谢！

Answer 2

原式=[(x+1)(x-1)/(x-1)^2+(1-x)/(x+1)]*(x-1)/x
=[(x+1)/(x-1)+(1-x)/(x+1)]*(x-1)/x
=[(x+1)^2-(x-1)^2]/(x-1)(x+1)*(x-1)/x
=[x^2+2x+1-x^2+2x-1]/(x+1)*1/x
=4x/(x+1)*1/x
=4/(x+1)