230问答网 > 简便计算(1+1⼀2+1⼀3+1⼀4)x(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)x(1⼀2+1⼀3+1⼀4)

简便计算(1+1⼀2+1⼀3+1⼀4)x(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)x(1⼀2+1⼀3+1⼀4)

2024-12-20 15:40:43

推荐回答（5个）

回答1：

为了简述方便

假设1/2+1/3+1/4=a

那么原式=(1+a)(a+1/5)-(1+a+1/5)a
=a+1/5+a*a+a/5-a-a*a-a/5
=1/5

回答2：

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

回答3：

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

回答4：

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

回答5：

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