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已知1/X+1/Y=5，求(2X-5XY+2Y)/(X+2XY+Y)的值

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收藏|2019/09/16 17:39

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2019/09/16 17:55

解 1/x+1/y=5 两边同时乘xy，得： x+y =5xy 整理 (2X-5XY+2Y)/(X+2XY+Y) =[2(x+y)-5xy]/(x+y+2xy] 把x+y=5xy代入(2X-5XY+2Y)/(X+2XY+Y)，得： =[10xy-5xy]/[5xy+2xy] =(5xy)/(7xy) =5/7 . 所以(2X-5XY+2Y)/(X+2XY+Y)的值为5/7.
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其他回答(10)
  • 虎哥19450909
    其他
    由已知等式两边都乘以xy得 x+y=5xy所以 (2X-5XY+2Y)/(X+2XY+Y)=[2(x+y)-5xy]/[(x+y)+2xy] =(10xy-5xy)/(5xy+2xy) =5xy/7xy=5/7
    回答于 2019/09/16 21:33
  • jtthh
    其他
    已知1/X+1/Y=5，则X+Y=5XY，2X+2Y=10XY(2X-5XY+2Y)/(X+2XY+Y)=(2X+2Y-5XY)/(X+Y+2XY)=(10XY-5XY)/(5XY+2XY)=(5XY)/(7XY)=5/7
    回答于 2019/09/16 21:21
  • 路石2014
    其他
    1/x+1/y=5x+y=5xy(2x-5xy+2y)/(x+2xy+y)=(10xy-5xy)/(5xy+2xy)=5/7
    回答于 2019/09/16 20:57
  • fff12345
    其他
    ∵1/x+1/y=5，∴y+x=5xy。(2x-5xy+2y)/(x+2xy+y)=[2(x+y)-5xy]/[(x+y)+2xy]=(2*5xy-5xy)/(5xy+2xy)=5xy/(7xy)=5/7
    回答于 2019/09/16 20:49
  • 特别成功
    其他
    已知1/X 1/Y=5， ( Y+X)/XY=5 X+Y=5XY(2X-5XY+2Y)/(X+2XY+Y)=(10XY-5XY)/(5XY+2XY)=5XY/(7XY)=5/7
    回答于 2019/09/16 20:18
  • 淘金沙
    其他
    这种题首先就是提取常数，之后再化简原式=[2（x+2xy+y）-9xy]/（x+2xy+y）=2-9xy/(x+2xy+y)对9xy/(x+2xy+y)分子和分母同除以xy后，得原式=2-9/（1/x+1/y+2）=2-9/7=5/7
    回答于 2019/09/16 19:54
  • js2018js
    其他
    1/x+1/y=5(x+y)/xy=5x+y=5xy(2x-5xy+2y)/(x+2xy+y)=(2*5xy-5xy)/(5xy+2xy)=5xy/7xy=5/7
    回答于 2019/09/16 19:42
  • 十九画1949
    其他
    解： 因为 1/x+1/y=5 所以 x+y=5xy 原式 （2x-5xy+2y)/(x+2xy+y) =[2(x+y)-5xy]/[(x+y)+2xy] =(10xy-5xy)/(5xy+2xy) =5xy/7xy =5/7.
    回答于 2019/09/16 19:12
  • 迈向宇
    其他
    本题：已知1/X+1/Y=5， 则：X+Y=5XY求：(2X-5XY+2Y)/(X+2XY+Y)=[2(X+Y)-5XY]/(X+Y+2XY)=[2(5XY)-5XY]/(5XY+2XY)=5XY/7XY=5/7
    回答于 2019/09/16 18:53
  • 药材王
    其他
    解答： ∵ 1/x+1/y=5 ∴ x+y=5xy 原式=（2x-5xy+2y)/(x+2xy+y) =[2(x+y)-5xy]/[(x+y)+2xy] =(10xy-5xy)/(5xy+2xy) =5xy/7xy =5/7。
    回答于 2019/09/16 18:20
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