已知:1/X+1/Y=5,求 2x-3xy+2y/x+2xy+y的值,

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已知:1/X+1/Y=5,求 2x-3xy+2y/x+2xy+y的值,

因为1/x+1/y=5
y/xy+x/xy=5
(x+y)/xy=5
所以
x+y=5xy
所以
(2x-3xy+2y)/(x+2xy+y)
=[2(x+y)-3xy]/[(x+y)+2xy]
=(2×5xy-3xy)/(5xy+2xy)
=(7xy)/(7xy)
=1

2x-3xy+2y 2(x+y)-3xy 2(1/x+1/y)-3 10-3
------------==------------------==-----------------=-------------------=1
x+2xy+y (x+y)+2xy 1/x+1/y+2 5+2