已知x分之1-y分之1=3,求（x-xy-y）分之（5x+xy-5y）的值

题目

已知x分之1-y分之1=3,求（x-xy-y）分之（5x+xy-5y）的值
要有过程

答案

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]
=[5*(-3xy)+xy]/[(-3xy)-xy]
=(-14xy)/(-4xy)
=7/2
=4