已知(1/x)-(1/y)=-2,求(3x+22xy-3y)/(x-14xy-y)的值

(y-x)/xy=-2
y-x=-2xy
x-y=2xy

(3x+22xy-3y)/(x-14xy-y)
=[3(x-y)+22xy]/[(x-y)-14xy]
=(6xy+22xy)/(2xy-14xy)
=28xy/(-12xy)
=-7/3

(1/x)-(1/y)=-2
两边乘
y-x=-2xy
x-y=2xy
所以(3x+22xy-3y)/(x-14xy-y)
=[3(x-y)+22xy]/[(x-y)-14xy]
=(3*2xy+22xy)/(2xy-14xy)
=28xy/(-12xy)
=-7/3

(1/x)-(1/y)=(y-x)/xy=-2

y-x=-2xy

设xy=a，则y-x=-2a

3x+22xy-3y=-3（y-x）+22xy=6a+22a=28a
x-14xy-y=-（y-x）-14xy=2a-14a=-12a
(3x+22xy-3y)/(x-14xy-y)=-7/3

(1/x)-(1/y)=-2
x-y=2xy
(3x+22xy-3y)/(x-14xy-y)=28xy/-12xy=-7/3