解方程1/(x^3+3x+2)+1/(x^3+5x+6)+1/(x^3+7x+12)=1/(x+4)

1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)=1/(x+4)
1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)=1/(x+4)
1/(x+1)-1/(x+4)=1/(x+4)
1/(x+1)=2/(x+4)
2(x+1)=x+4
2x+1=x+4
2x-x=4-1
x=3
经检验,x=3是原方程的解