简便算法(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)怎么算

Answer 1

原式=（1+1/2+1/3+1/4）*(1/2+1/3+1/4+1/6)-(1+1/2+1/3+1/4)*(1/2+1/3+1/4)-(1/5)*(1/2+1/3+1/4)
=（1+1/2+1/3+1/4）*(1/6)-(1/5)*(1/2+1/3+1/4)
=1/6+(1/2+1/3+1/4）*(1/6)-(1/5)*(1/2+1/3+1/4)
=1/6+(1/2+1/3+1/4）*(-1/30)
=47/360

Answer 2

设1/2+1/3+1/4=13/12=x
原式=（1+x)*(x+1/6)-(1+x+1/5)*x
=x的平方+7x/6+1/6-x的平方-6x/5
=1/6-1/30x
=1/6-1/30*13/12
=47/360

Answer 3

设(1/2+1/3+1/4)＝a (1/2+1/3+1/4+1/6)＝b
则原式＝﹙1＋a﹚b-﹙1＋b﹚a
＝b＋ab－ab－a
＝b－a
＝1/2+1/3+1/4+1/6-1/2+1/3+1/4
＝1/6
思路是这样的，是不是你打错一个数