有这样一道题“计算x2−2x+1x2−1÷x−1x2+x−x的值，其中x=2005”．甲同学把条件“x=2005”错抄成”x=2050“，但他的计算结果也是正确的，你说这是怎么回事？试一试，你就会有收获．

Question

(x2−2x+1)/(x2−1)÷(x−1)/(x2+x)−x的值，其中x=2005”．甲同学把条件“x=2005”错抄成”x=2050“，但他的计算结果也是正确的，你说这是怎么回事？试一试，你就会有收获．(x2−2x+1)/(x2−1)x2−2x+1x2−2x+1x2−2x+1x2−2x+12−2x+1x2−1x2−1x2−1x2−12−1(x−1)/(x2+x)x−1x−1x2+xx2+xx2+xx2+x2+x

Answer 1

原式=((x−1)2)/((x+1)(x−1))×(x(x+1))/(x−1)-x
=x-x
=0．
即原代数式的值与x的取值无关．
故甲同学把x的值抄错结果仍正确． ((x−1)2)/((x+1)(x−1))(x−1)2(x−1)2(x−1)22(x+1)(x−1)(x+1)(x−1)(x+1)(x−1)×(x(x+1))/(x−1)x(x+1)x(x+1)x(x+1)x−1x−1x−1-x
=x-x
=0．
即原代数式的值与x的取值无关．
故甲同学把x的值抄错结果仍正确．