化简1/x(x+3)+1/(x+3)(x+6)+1/(x+6)(x+9)+…+1/(x+96)(x+99)
问题描述：
化简1/x(x+3)+1/(x+3)(x+6)+1/(x+6)(x+9)+…+1/(x+96)(x+99)
要过程
答
原式＝(1/3)[1/X-1/(X+3)]+(1/3)[1/(X+3)-1/(X+6)]+……+(1/3)[1/(X+96)-1/(X+99)]=(1/3)[1/X-1/(X+3)+1/(X+3)-1/(X+6)+……+1/(X+96)-1/(X+99)]=(1/3)[1/X-1/(X+99)]=(1/3)[99/X(X+99)]=33/X(X+99)