Question

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

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

也要简算,过程

Answer 1

上面的错了，应该是：
令（1+1/2+1/3+1/4)＝a，(1/2+1/3+1/4+1/5）＝b
原式＝ab－（a＋1/5)*(b-1/5)
=ab-(ab+1/5b-1/5a-1/25)
=ab-ab-1/5b+1/5a+1/25
=1/5(a+b)+1/25
=1/5*4/5+1/25
=4/25+1/25
=1/5

Answer 2

解：原式=1*（1/2+1/3+1/4+1/5）+（1/2+1/3+1/4）*（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）
=1/2+1/3+4/4+1/5-1/2-1/3-1/4
=1/5
本座是你班长

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

Answer 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+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)=a,(1/2+1/3+1/4)=b

(1+1/2+1/3+1/4)乘(1/2+1/3+1/4+1/5)-（1+1/2+1/3+1/4+1/5）乘(1/2+1/3+1/4)
=a*(b+1/5)-(a+1/5)*b
=ab+a/5-ab-b/5
=(a-b)/5
=1/5

Answer 5

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