简算(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÷

问题描述:

简算(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÷
简算(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 )

把1÷2+1÷3+1÷4看成一个整体,可以用一字母如A代替,则式子转变为
(1+A)×(A+1÷5)-(1+A+1÷5)×A=(1+A)×(A+1÷5)-(A+1÷5)×A-A=1÷5