230问答网 > (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)

(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)

要简算，过程

2024-12-04 04:44:38

推荐回答（4个）

回答1：

设1/2+1/3+1/4=x
1/2+1/3+1/4+1/5=y
(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+x)y-(1+y)x
=y+xy-x-xy
=y-x
=1/5

回答2：

解:设1/2+1/3+1/4+1/5=a.
则原式=(1+a-1/5)a-(1+a)(a-1/5)
=a+a²-(1/5)a+(1/5)+(1/5)a-a-a²
=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+1/2+1/3+1/4)*(1+1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4)-(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4)
=(1+1/2+1/3+1/4+1/5)*[(1+1/2+1/3+1/4)-(1/2+1/3+1/4)]-(1+1/2+1/3+1/4)
==(1+1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4)
=1/5

回答4：

1/5