已知1/X-1/Y=5 ,则x-2xy-y/4x+3xy-4y

题目

已知1/X-1/Y=5 ,则x-2xy-y/4x+3xy-4y

答案

1/x-1/y=(y-x)/xy=5
y-x=5xy
x-y=-5xy
所以原式=[(x-y)-2xy]/[4(x-y)+3xy]
=[(-5xy)-2xy]/[4(-5xy)+3xy]
=-7xy/(-17xy)
=7/17