若1/x-1/y=1,求3y-xy-3x/x-xy-y的值

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若1/x-1/y=1,求3y-xy-3x/x-xy-y的值
若1/x-1/y=1,求3y-xy-3x/x-xy-y的值

若1/x-1/y=1,求3y-xy-3x/x-xy-y的值
1/x-1/y=1
(y-x)/(xy)=1
y-x=xy
x-y=-xy
(3y-xy-3x)/(x-xy-y)
=[3(y-x)-xy]/[(x-y)-xy]
=(3xy-xy)/(-xy-xy)
=(2xy)/(-2xy)
=-1


∵1/x-1/y=1
两边乘以xy可得
y-x=xy
所以
(3y-xy-3x)/(x-xy-y)
=[3(y-x)-xy]/[-(y-x)-xy]
=(3xy-xy)/(-xy-xy)
=2xy/(-2xy)
=-1

由“1/x-1/y=1”可得到y-x=xy
把xy=y-x代入第2式，可得到：2(y-x)/2(x-y)=-1

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