简便计算(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...
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
请简便计算:(1+1\/2+1\/3+1\/4)(1\/2+1\/3+1\/4+1\/5)-(1+1\/2+1\/3+1\/4+1\/...
=(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
(1+1\/2+1\/3+1\/4)*(1\/2+1\/3+1\/4+1\/5)怎么做,求讲解 !
解：令a=1\/2+1\/3+1\/4 则1+1\/2+1\/3+1\/4=1+a 1\/2+1\/3+1\/4+1\/5=a+1\/5 1+1\/2+1\/3+1\/4+1\/5=1+a+1\/5 所以原式=(1+a)(a+1\/5)-a(1+a+1\/5)=a(1+a)+(1+a)*1\/5-a(1+a)-a*1\/5 =(1+a)*1\/5-a*1\/5 =1\/5+a*1\/5-a*1\/5 =1\/5 ...
(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)= (25\/12) * 77\/60=385\/144
求高手解题:(1+1\/2+1\/3+1\/4)×(1\/2+1\/3+1\/4+1\/5)—(1+1\/2+1\/3+1\/4...
令a=1\/2+1\/3+1\/4 则原式=(1+a)(a+1\/5)-(1+a+1\/5)a =(1+a)a+1\/5(1+a)-(1+a)-1\/5a =1\/5(1+a)-1\/5a =1\/5+1\/5a-1\/5a =1\/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...
（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） (加1减1)=（1+1\/2+1\/3+1\/4）X（1-1+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)*(1+1\/2+1\/3+1\/4+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\/...
设1+1\/2+1\/3+1\/4=x 1\/2+1\/3+1\/4+1\/5=y 则原式=xy-(1+y)(x-1)=xy-xy-x+y+1 =y-x+1 =1\/5
(1+1\/2+1\/3+1\/4)x(1\/2+1\/3+1\/4+1\/5)一(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\/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 望采纳O(∩_∩)O~...
(1+1\/2+1\/3+1\/4)*(1\/2+1\/3+1\/4+1\/6)—(1+1\/2+1\/3+1\/4+
设 (1+1\/2+1\/3+1\/4)=a (1\/2+1\/3+1\/4)=b 则a-b=1 把a,b代入上面式子得 a(b+1\/5)-(a+1\/5)b =ab+1\/5a-ab-1\/5b =1\/5(a-b)=1\/5
(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\/...
令a=1\/2+1\/3+1\/4 则1+1\/2+1\/3+1\/4=1+a 1\/2+1\/3+1\/4+1\/5=a+1\/5 1+1\/2+1\/3+1\/4+1\/5=1+a+1\/5 所以原式=(1+a)(a+1\/5)-a(1+a+1\/5)=a(1+a)+(1+a)*1\/5-a(1+a)-a*1\/5 =(1+a)*1\/5-a*1\/5 =1\/5+a*1\/5-a*1\/5 =1\/5 ...
