一道算式请用简便方法,(1+1/2+1/3+1/4)×(1/2+1/3+1/4+1/6)-(1+1/2+1/3+1/4+1/5)×_数学解答

一道算式请用简便方法,
(1+1/2+1/3+1/4)×(1/2+1/3+1/4+1/6)-(1+1/2+1/3+1/4+1/5)×(1/2+1/3+1/4)=?

人气：186 ℃　时间：2020-04-01 16:24:45

解答

设x=1+1/2+1/3+1/4=25/12y=1/2+1/3+1/4=13/12
原式=x*(y+1/6)-(x+1/5)*y
=xy+1/6x-xy-1/5y
=1/6x-1/5y
=1/6*25/12-1/5*13/12*
=47/360