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（y-x）/xy=4是如何求出来的,知道是通分.还有y-x=4xy x-y=-4xy又是如何求出来的?
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1/x-1/y=4
左边通分得到
y/xy-x/xy=4
于是得到(y-x)/xy=4
两边同时乘以xy得到
y-x=4xy
两边同时乘以-1
得到x-y=-4xy
求值：(2x+xy-2y)/(x-2xy-y)
=[2(x-y)+xy]/[(x-y)-2xy]
带入x-y=-4xy
=[-8xy+xy]/(-4xy-2xy)
=(-7xy)/(-6xy)
=7/6如果有疑问请点【评论】或者【追问】
======以下答案可供参考======
供参考答案1:
∵1/x-1/y=4
∴两分式分子分母同时乘以x或y得y/xy-x/xy=4
∴(y-x)xy=4
∴等式两端同时乘以xy得y-x=4xy
∴等式两端同时乘以-1得x-y=-4xy
供参考答案2:
∵1/x-1/y=4
通分,公分母xy,1/x分子分母同乘以y,1/y分子分母同乘以x,
y/xy-x/xy=4
∴(y-x)/xy=4
两边同乘以xy,去分母,
∴y-x=4xy
两边同乘以-1,
-(y-x)=-4xy-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