已知1/x-1/y=3,求(2x-3xy-2y)/(x-2xy-y)
问题描述：
已知1/x-1/y=3,求(2x-3xy-2y)/(x-2xy-y)
答
等于1.8
(2x-3xy-2y)/(x-2xy-y)
=2 + xy/(x-2xy-y)
=2 + 1/(1/y-2-1/x)
=2 + 1/(-3-2)
=1.8
答
1/x-1/y=3
∴(y-x)/xy=3,即y-x=3xy
∴x-y=-3xy
∴(2x-3xy-2y)/(x-2xy-y)
=[2(x-y)-3xy]/[(x-y)-2xy]
=(-6xy-3xy)/(-3xy-2xy)
=9/5