计算1/x×(x+3)+1/(x+3)×(x+6)+1/(x+6)×(x+9)+1/(x+9)×(x+12)

问题描述:

计算1/x×(x+3)+1/(x+3)×(x+6)+1/(x+6)×(x+9)+1/(x+9)×(x+12)

1/x×(x+3)=(1/x-1/(x+3))/3
1/(x+3)×(x+6)=1/(1+3)x-1/(x+6))/3
……
以此类推,原式=(1-1/(x+12))/3=(x+11)/(3x+36)