I would say you split 1/(x*(x+3))=1/(3*x)-1/(3*(x+3))=1/3*(1/x-1/(x+3)). Now if you sum over these terms everything cancels out except 1/3*(1/1+1/2+1/3)=11/18
I would say you split 1/(x*(x+3))=1/(3*x)-1/(3*(x+3))=1/3*(1/x-1/(x+3)). Now if you sum over these terms everything cancels out except 1/3*(1/1+1/2+1/3)=11/18