解方程:(x²+x+1)/(x²+1)+(2x²+x+2)/(x²+x+1)=1

:(x²+x+1)/(x²+1)+(2x²+x+2)/(x²+x+1)=19/6:(x²+x+1)/(x²+1)+(x²+x+1+x²+1)/(x²+x+1)=19/6:(x²+x+1)/(x²+1)+1+ (x²+1)/(x²+x+1)=19/6设:(x²+x+1)/(x²+1)=y∴原方程可化为y +1+1/y=19/66y²-13y+6=0(3y-2)(2y-3)=0∴y=2/3 y=3/2∴:(x²+x+1)/(x²+1)=2/3 :(x²+x+1)/(x²+1)=3/22x²+2=3x²+3x+3 3x²+3=2x²+2x+2x²+3x+1=0 x²-2x+1=0x=(-3±√5)/2 x=1