已知1/x-1/y=3,求(3x+4xy-3y)/(x-2xy-y)的值

题目

已知1/x-1/y=3,求(3x+4xy-3y)/(x-2xy-y)的值

答案

1/x-1/y通分=(y-x)/xy=3
y-x=3xy
x-y=-3xy
所以原式=[3(x-y)+4xy]/[(x-y)-2xy]
=[3(-3xy)+4xy]/[(-3xy)-2xy]
=-5xy/(-5xy)
=1