已知1/x=1/y+3,则(5x+xy-5y)/(x-xy-y)的值为（ ）

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已知1/x=1/y+3,则(5x+xy-5y)/(x-xy-y)的值为（ ）
已知1/x=1/y+3,则(5x+xy-5y)/(x-xy-y)的值为（ ）

已知1/x=1/y+3,则(5x+xy-5y)/(x-xy-y)的值为（ ）
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)
=(1-5(1/x-1/y))/(-1-(1/x-1/y))
=(1-15)/(-1-3)
=14/4
=7/2

(5x+xy-5y)/(x-xy-y)把分子分母同除以xy
分子变为5/y+1-5/x=1+5(1/y-1/x)
分母变为 1/y-1-1/x
1/y-1/x=-3
所以 (1-15)/(-3-1)=7/2

7/2

由1/x=1/y+3，两边同时乘xy可知y=x+3xy，x-y=-3xy，代入得
(5x+xy-5y)/(x-xy-y)=（-15xy+xy）/(-3xy-xy)=7/2

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