已知,1/x+1/y=5.,求分式3x+xy+3y/x-2xy+y的值

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已知,1/x+1/y=5.,求分式3x+xy+3y/x-2xy+y的值已知,1/x+1/y=5.,求分式3x+xy+3y/x-2xy+y的值已知,1/x+1/y=5.,求分式3x+xy+3y/x-2x

已知,1/x+1/y=5.,求分式3x+xy+3y/x-2xy+y的值
已知,1/x+1/y=5.,求分式3x+xy+3y/x-2xy+y的值

已知,1/x+1/y=5.,求分式3x+xy+3y/x-2xy+y的值
首先化简通分1/x+1/y=5得:
(x+y)/xy=5
即有x+y=5xy
将要求的分式化简:
3x+xy+3y/x-2xy+y
=3x+3y+xy/x+y-2xy (根据加法交换律)
=3(x+y)+xy/(x+y)-2xy
=15xy+xy/5xy-2xy(将x+y=5xy代入)
=16xy/3xy
=16/3

1/x+1/y=5
x+y=5xy
3x+xy+3y/x-2xy+y
=3x+3y+xy/x+y-2xy (根据加法交换律)
=3(x+y)+xy/(x+y)-2xy
=15xy+xy/5xy-2xy(将x+y=5xy代入)
=16xy/3xy
=16/3