已知x²+x-1=0,求x(1-2除以1-x)除以(x+1)-x(x²-1)除以x平方-2x+1的值

2024-12-16 12:44:22
推荐回答(3个)
回答1:

x²+x-1=0,所以x²=-(x-1)
x(1-2除以1-x)除以(x+1)-x(x²-1)除以x平方-2x+1
=-x(1+x)除以(1-x)除以(x+1)-x(x+1)(x-1)除以(x-1)²
=x/(x-1)-x(x+1)/(x-1)
=x(1-x-1)/(x-1)
=-x²/(x-1)
=-(x-1)/(x-1)
=-1

回答2:

x²+x-1=0,x-1=-x²
x(1-2/(1-x))/(x+1)-x(x²-1)/(x²-2x+1)=x[(1-x-2)/(1-x)]/(x+1)-x(x-1)(x+1)/(x-1)²
=x/(x-1)-x(x+1)/(x-1)=x(1-x-1)/(x-1)=-x²/(x-1)=1

回答3:

x[1-2/(1-x)]/(x+1)]-x(x²-1)/(x²-2x+1)=x(x+1)/(x-1)-x(x²-1)/(x-1)²=x(x+1)/(x-1)-x(x+1)/(x-1)=0.