受此启发,解方程1/x²+3x+2 +1/x²+5x+6 +1/x²+7x+12=1/3x 貌似关于部分分式好像

1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)=1/3x
1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)=1/3x
1/(x+1)-1/(x+4)=1/3x
3x²+12x-3x²-3x=x²+5x+4
x²-4x+4=0
(x-2)²=0
x=2