Question

若实数x,y满足1/x-1/y=5,则分式3x-2xy-3y/x+xy-y的值等于?

Answer 1

1/x-1/y=5

即,(y-x)/xy=5

即,x-y=-5xy

(3x-2xy-3y)/(x+xy-y)

=[3(x-y)-2xy]/[(x-y)+xy]

=(-15xy-2xy)/(-5xy+xy)

=(-17xy)/(-4xy)

=17/4

所以,分式3x-2xy-3y/x+xy-y的值等于17/4