Question

先化简，在求值:（1/x+x²-2x+1/x²-1）÷x-1/x+1，其中x=2.

先化简，在求值:（1÷x+1 + x²-2x+1÷ x²-1）÷ x-1÷x+1，其中x=2.答案等于2，x²-2x+1这一步请详细讲解。

Answer 1

（1÷x+1 + x²-2x+1÷ x²-1）÷ x-1÷x+1

=（1/(x+1)+(x-1)²/(x-1)(x+1)）×(x+1)/(x-1)
=（1/(x+1)+(x-1)/(x+1)）×(x+1)/(x-1)
=（x/(x+1)）×(x+1)/(x-1)
=x/(x-1)
=2÷(2-1)
=2

Answer 2

原式=(1/x+(x-1)²/(x+1)(x-1))×(x+1)/(x-1)
=(1/x+(x-1)/(x+1))×(x+1)/(x-1)
=(x+1)/x(x-1)+1
=(x+1+x²-x)/x(x-1)
=(x²+1)/x(x-1)
=(4+1)/2(2-1)
=5/2;

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答案是2，你错了

追答

你给的题目是什么？你给的题目算出来是这个，你上面和下面题目不一样，下面解如下：
（1÷x+1 + x²-2x+1÷ x²-1）÷ x-1÷x+1

=（1/(x+1)+(x-1)²/(x-1)(x+1)）×(x+1)/(x-1)
=（1/(x+1)+(x-1)/(x+1)）×(x+1)/(x-1)
=（x/(x+1)）×(x+1)/(x-1)
=x/(x-1)
=2÷(2-1)
=2