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+x²-2x+1/x²-1）÷x-1/x+1，其中x=2.

Answer 1

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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Answer 2

[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=2

原式=3/2+1
=5/2

Answer 3

（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