若1/x-1/y=1/3,求(2x+3xy-2y)/(x-3xy-y)

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若1/x-1/y=1/3,求(2x+3xy-2y)/(x-3xy-y)

若1/x-1/y=1/3,求(2x+3xy-2y)/(x-3xy-y)
若1/x-1/y=1/3,求(2x+3xy-2y)/(x-3xy-y)

若1/x-1/y=1/3,求(2x+3xy-2y)/(x-3xy-y)
1/x-1/y=1/3
(2x+3xy-2y)/(x-3xy-y)
分子分母同除以xy:
= {2/y+3-2/x} / {1/y-3-1/x}
= {-2(1/x-1/y)+3} /{ -(1/x-1/y)-3}
= {-2*1/3+3} / {-1/3-3}
= {-2+9} / {-1-9}
= -7/10

最简单的方法
(2x+3xy-2y)/(x-2xy-y)
分子分母同时除以xy,得:
=[(2/y-2/x)+3]/[(1/y-1/x)-2]
=[-2(1/x-1/y)+3)/[-(1/x-1/y)-2]
=(-6+3)/(-3-2)
=3/5