若1/X-1/Y=3,求5X+2XY-5Y/X-4XY-Y
问题描述：
若1/X-1/Y=3,求5X+2XY-5Y/X-4XY-Y
答
1/X-1/Y=3
通分（Y-X）/XY=3
所以Y-X=3XY
5X+2XY-5Y/X-4XY-Y
=5X-5Y+2XY/X-Y-4XY
=5（X-Y）+2XY/(X-Y)-4XY
=[5*(-3XY)+2XY]/-3XY-4XY
=(-15XY+2XY)/-7XY
=-13XY/-7XY
=-13/-7
=13/7
答
因为1/x-1/y=3
两边乘以xy得y-x=3xy, x-y=-3xy
所以原式=[5(x-y)+2xy]/(x-y-4xy)
=(-5*3xy+2xy)/(-3xy-4xy)
=(-13xy)/(-7xy)
=13/7