已知1/x+1/y=3,求x+xy+y/2x-3xy+2y的值

已知1/x+1/y=3,求x+xy+y/2x-3xy+2y的值
已知1/x+1/y=3,求x+xy+y/2x-3xy+2y的值

已知1/x+1/y=3,求x+xy+y/2x-3xy+2y的值
(x+xy+y)/(2x-3xy+2y) 的上下各项均除以 xy 得
(1/y+1+1/x)/(2/y-3+2/x)
= (1+3)/(6-3)
= 4/3
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(x+xy+y)/(2x-3xy+2y) 分子分母同时除以xy
=(1/y+1+1/x)/(2/y-3+2/x)=(3+1)/(6-3)=4/3

x+xy+y/2x-3xy+2y
=(1/y+1+1/x)/(2/y-3+2/x)
=4/3