Question

(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)求解

(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)求解

Answer 1

因式分解
(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(1/2+1/3+1/4+1/5）+ (1/2+1/3+1/4) x(1/2+1/3+1/4+1/5) -[1 x(1/2+1/3+1/4)+(1/2+1/3+1/4+1/5)x(1/2+1/3+1/4)]
=1 x(1/2+1/3+1/4+1/5）+ (1/2+1/3+1/4) x(1/2+1/3+1/4+1/5) -1 x(1/2+1/3+1/4)-(1/2+1/3+1/4+1/5)x(1/2+1/3+1/4)
=(1/2+1/3+1/4+1/5)-(1/2+1/3+1/4)
=1/5

Answer 2

（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+1/5)-(1+1/2+1/3+1/4)-(1+1/2+1/3+1/4+1/5）X（1/2+1/3+1/4） (第一项与第三项合并)
=(1+1/2+1/2+1/4+1/5)*1-(1+1/2+1/3+1/4)
=1/5

41.2X8.1+11X9.25+537X0.19
=412*0.81+11*9.25+537*0.19
=412*0.81+11*9.25+(412+125)*0.19
=412*(0.81+0.19)+11*9.25+125*0.19
=412+11*9.25+125*0.19
=412+11*(8+1.25)+1.25*19
=412+88+11*1.25+1.25*19
=500+1.25*(11+19)
=500+1.25*30
=500+37.5
=537.5

Answer 3

看好思路：
设：1+1/2+1/3+1/4 = A
1/2+1/3+1/4 = B
原式可变为：
A*(B+1/5)-(A+1/5)*B
=AB+(1/5)*A-AB-(1/5)*B
=(1/5)*A-(1/5)*B
=(1/5)*(A-B)
=(1/5)*(1)
=1/5

遇到这种问题一定要学会化简，否则难做还容易出错。

Answer 4

(1+1/2+1/3+1/4)×(1/2+1/3+1/4）+(1+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=1/5