Question

简便计算（1+1/2+1/3+1/4）×（1/2+1/3+1/4+1/5）-（1+1/2+1/3+1/4+1/5）×（1/2+1/3+1/4）

要过程！！急，过程要清楚

Answer 1

设a=（1/2+1/3+1/4），b=（1/2+1/3+1/4+1/5）
原式=（1+a）*b-（1+b）*a
=b+ab-a-ab
=b-a
=1/5

追问

要小学的，中学的太深奥

追答

(1+1/2+1/3+1/4)x(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)x(1/2+1/3+1/4)
=(1+1/2+1/3+1/4)x(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4)x(1/2+1/3+1/4)-1/5 x(1/2+1/3+1/4)
=(1+1/2+1/3+1/4) x(1/2+1/3+1/4+1/5-1/2-1/3-1/4)-1/5 x(1/2+1/3+1/4)
=(1+1/2+1/3+1/4) x1/5-1/5 x(1/2+1/3+1/4)
=1/5 x(1+1/2+1/3+1/4-1/2-1/3-1/4)
=1/5 x1
=1/5