已知1/x-1/y=4,求(2x+xy-2y)/(x-2xy-y)

已知1/x-1/y=4,求(2x+xy-2y)/(x-2xy-y)
已知1/x-1/y=4,求(2x+xy-2y)/(x-2xy-y)

已知1/x-1/y=4,求(2x+xy-2y)/(x-2xy-y)
∵1/x-1/y=4
∴(y-x)/xy=4
∴y-x=4xy
∴x-y=-4xy
(2x+xy-2y)/(x-2xy-y)
=[2(x-y)+xy]/[(x-y)-2xy]
=(-8xy+xy)/(-4xy-2xy)
=(-7xy)/(-6xy)
=7/6
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1/x-1/y=y-x/xy=4
x-y/=-4xy
(2x+xy-2y)/(x-2xy-y)
=[2(x-y)+xy]/(x-y-2xy)
=[2(-4xy)+xy]/(-4xy-2xy)
=7/6

1/x-1/y=4,xy≠0
同×xy,y-x=4xy
(2x+xy-2y)/(x-2y-y)=(-8xy+xy)/(-4xy-2xy)=7/6