1/x-1/y=3求 （5x+xy-5y)/(x-xy-y)的值

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1/x-1/y=3求 （5x+xy-5y)/(x-xy-y)的值

1/x-1/y=3求 （5x+xy-5y)/(x-xy-y)的值
1/x-1/y=3
求 （5x+xy-5y)/(x-xy-y)的值

1/x-1/y=3求 （5x+xy-5y)/(x-xy-y)的值
1/x-1/y=3
(y-x)/xy=3
y-x=3xy
x-y=-3xy
（5x+xy-5y)/(x-xy-y)
=[5(x-y)+xy]/[(x-y)-xy]
=(-15xy+xy)/(-3xy-xy)
=-14xy/(-4xy)
=7/2

(5x+xy-5y)/(x-xy-y)
=(5/y+1-5/x)/(1/y-1-1/x)
=(1-3)/(-1-3)
=1/2

(1)式等号两边乘以xy得 y-x=3xy
带到（2）式得 -14xy/(-4xy)=7/2

因为
1/x-1/y=3
所以
y-x=3xy
所以
（5x+xy-5y)/(x-xy-y)
=(xy-15xy)/(-3xy-xy)
=-14xy/-4xy
=7/2

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