230问答网 > 简便运算：(1+1⼀2+1⼀3+1⼀4)*(1⼀2+1⼀3+1⼀4+1⼀5)-(1+1⼀2+1⼀3+1⼀4+1⼀5)*（1⼀2+1⼀3+1⼀4）

简便运算：(1+1⼀2+1⼀3+1⼀4)(1⼀2+1⼀3+1⼀4+1⼀5)-(1+1⼀2+1⼀3+1⼀4+1⼀5)（1⼀2+1⼀3+1⼀4）

2024-12-17 05:33:07

推荐回答（3个）

回答1：

(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）
解设(1+1/2+1/3+1/4+1/5)=t
原式可变形为
(t-1/5)(t-1)-t(t-1/5-1)
=t-t+1/5
=1/5

回答2：

(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）

=(1/2+1/3+1/4)*(1/2+1/3+1/4+1/5)+(1/2+1/3+1/4+1/5)-(1/2+1/3+1/4)*(1/2+1/3+1/4+1/5)-(1/2+1/3+1/4)
=（1/2+1/3+1/4+1/5）-（1/2+1/3+1/4）
=1/5

回答3：

（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）

=（1/2+1/3+1/4）×(1/2+1/3+1/4+1/5)+(1/2+1/3+1/4+1/5)－（1+1/2+1/3+1/4+1/5）×（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）+(1/2+1/3+1/4+1/5)

=-1*(1/2+1/3+1/4)+1/2+1/3+1/4+1/5

=1/5