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)=[x+3+ x+1+x+2]/[(x+1)(x+2)(x+3)]=(3x+6)/[(x+1)(x+2)(x+3)]=3/[(x+1)(x+3)]