Question

有这样一道题:计算[(x^2-2x+1)/(x^2-1)]/[(x-1)/(x^2+x)]-x的值

有这样一道题:计算[(x^2-2x+1)/(x^2-1)]/[(x-1)/(x^2+x)]-x的值，其中x=2006.小明把x=2006抄错成x=2060，但他的计算结果也是正确的。请你说说为什么

Answer 1

[(x^2-2x+1)/(x^2-1)]/[(x-1)/(x^2+x)]-x
=[(x-1)^2/[(x-1)(x+1)]]/[(x-1)/[x(x+1)]-x
=[(x-1)/(x+1)]*[x(x+1)/(x-1)]-x
=x-x
=0
由于化简后为常数
与x值无关