x/x^2+x+1=-1/22x^2/(x^2-x+1)+x-1/x^3-1

问题描述:

x/x^2+x+1=-1/22x^2/(x^2-x+1)+x-1/x^3-1

x/(x^2+x+1)=-1/2x^2+x+1=-2x则x^2-x+1=-4x且x^2+1=-3x2x^2/(x^2-x+1)+(x-1)/(x^3-1)=2x^2/(x^2-x+1)+(x-1)/(x-1)(x^2+x+1)=2x^2/(x^2-x+1)+1/(x^2+x+1)=2x^2/(-4x)+1/(-2x)=-x/2-1/2x=-(x^2+1)/2x=-(-3x)/2x=3/2