1/(x+1)(x+2)+1/(x+2)(x+3)=2/3,
——》[1/(x+1)-1/(x+2)]+[1/(x+2)-1/(x+3)]=2/3
——》1/(x+1)-1/(x+3)=2/3
——》2/(x+1)(x+3)=2/3
——》(x+1)(x+3)=3
——》x^2+4x=0,
——》x1=-4,x2=0.