Question

简便计算： （1+1/3+1/5+1/7)x(1/3+1/5+1/7+1/9)-(1+1/3+1/5+1/7+1/9)x(1/3+1/5+1/7)

对的追加分值！！！

Answer 1

设1/3+1/5+1/7=t
（1+1/3+1/5+1/7)x(1/3+1/5+1/7+1/9)-(1+1/3+1/5+1/7+1/9)x(1/3+1/5+1/7)
=(1+t)x(t+1/9)-(1+t+1/9)xt
=1x(t+1/9)+tx(t+1/9)-[1+(t+1/9)]xt
=t+1/9+tx(t+1/9)-t-(t+1/9)xt
=t-t+tx(t+1/9)-(t+1/9)xt+1/9
=1/9

追问

脱式计算，谢谢

Answer 2

设x=1/3+1/5+1/7, y=1/3+1/5+1/7+1/9
原式=(1+x)y-(1+y)x=y-x=1/9

Answer 3

设x=1/3+1/5+1/7
y=1/3+1/5+1/7+1/9
（1+1/3+1/5+1/7)x(1/3+1/5+1/7+1/9)-(1+1/3+1/5+1/7+1/9)x(1/3+1/5+1/7)
=(1+x)y-(1+y)x
=y+xy-x-xy
=y-x
=1/9