一道算式请用简便方法,
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/06/22 08:46:41
一道算式请用简便方法,
(1+1/2+1/3+1/4)×(1/2+1/3+1/4+1/6)-(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+1/6)-(1+1/2+1/3+1/4+1/5)×(1/2+1/3+1/4)=?
![一道算式请用简便方法,](/uploads/image/z/16214007-39-7.jpg?t=%E4%B8%80%E9%81%93%E7%AE%97%E5%BC%8F%E8%AF%B7%E7%94%A8%E7%AE%80%E4%BE%BF%E6%96%B9%E6%B3%95%2C)
设x=1+1/2+1/3+1/4=25/12 y=1/2+1/3+1/4=13/12
原式=x*(y+1/6)-(x+1/5)*y
=xy+1/6x-xy-1/5y
=1/6x-1/5y
=1/6*25/12-1/5*13/12*
=47/360
原式=x*(y+1/6)-(x+1/5)*y
=xy+1/6x-xy-1/5y
=1/6x-1/5y
=1/6*25/12-1/5*13/12*
=47/360