题目

先化简再求值(3/x+1-x+1)除以x^2-2x/x+1其中x满足方程x/x-1+1/x=1

提问时间：2021-01-02

答案

先化简再求值(3/x+1-x+1)除以x^2-2x/x+1其中x满足方程x/x-1+1/x=1
x/x-1+1/x=1
x*x+(x-1)=x(x-1)
x^2+x-1=x^2-x
2x=1
x=1/2
(3/x+1-x+1)/(x^2-2x)/(x+1)
=[3/(x+1)-(x-1)(x+1)/(x+1)]*[(x+1)/x(x-2)]
=[(3-x^2+1)/(x+1)]*[(x+1)/x(x-2)]
=[(2+x)(2-x))/(x+1)]*[(x+1)/x(x-2)]
=-(2+x)/x
=-(2+1/2)/(1/2)
=-5