已知1/x+1/y=5,求(2x-3y+2y)/(x+2xy+y)的值

问题描述:

已知1/x+1/y=5,求(2x-3y+2y)/(x+2xy+y)的值

题目是否抄错?应该是(2X-3XY+2Y)/(X+2XY+Y)吧?
1/X+1/Y=5
(Y+X)/XY=5
X+Y=5XY
(2X-3XY+2Y)/(X+2XY+Y)
=〔2(X+Y)-3XY〕/(X+Y+2XY)
=(10XY-3XY)/(5XY+2XY)
=7XY/7XY
=1