这个题目就是利用乘法分配律:
(1+1/2+1/3+1/4)*(1/2+1/3+1/4+1/5)-(1+1/2+1/旦伍薯3+1/4+1/5)*(1/2+1/3+1/4)
因为每项里面都有(橘晌1/2+1/3+1/4)这一项,所以可以将之看成公因式提出来:
所以原式=[1+(1/2+1/3+1/4)]*[1/5+(1/2+1/3+1/4)] - [6/5+(1/2+1/3+1/模者4)]*(1/2+1/3+1/4)
=(1/2+1/3+1/4)^2 + 6/5(1/2+1/3+1/4)+ 1/5 - [(1/2+1/3+1/4)^2+ 6/5(1/2+1/3+1/4)]
=1/5