1/(x^2+3x+2)+1/(x^2+5x+6)+1/(x^2+4x+3)=1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+1)(x+3)=1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+1)(x+3)=1/(x+1)-1/(x+3)+1/(x+1)(x+3)=(x+3)/(x+1)(x+3)-(x+1)/(x+1)(x+3)+1/(x+1)(x+3)=[...