已知x的平方+x-1=0,求x[(1-2/1-x)/(x+1)-x的平方-1/x的平方-2x+1]的值_数学解答

已知x的平方+x-1=0,求x[(1-2/1-x)/(x+1)-x的平方-1/x的平方-2x+1]的值

人气：257 ℃　时间：2020-05-24 09:53:15

解答

x{[1-2/(1-x)]/(x+1)-(x^2-1)/(x^2-2x+1)}
=x{[-(x+1)/(1-x)]/(x+1)-(x-1)(x+1)/(x-1)^2}
=x{-1/(1-x)-(x+1)/(x-1)}
=-x^2/(x-1),
因为x^2+x-1=0,
所以x^2=-(x-1),
所以原式=1.