分式?????????

来源：百度知道编辑：UC知道时间：2024/06/08 11:26:06

已知1/X+1/Y=5,,则2X-5XY+2Y/X+2XY+Y的值是多少

1/X+1/Y=5
(X+Y)/XY=5
X+Y=5XY

2X-5XY+2Y/X+2XY+Y
=[2(X+Y)-5XY]/[(X+Y)+2XY]
=(10XY-5XY)/(5XY+2XY)
=5XY/7XY
=5/7

因为1/X+1/Y=5

所以x+y=5xy

所以
2X-5XY+2Y/X+2XY+Y

=(10xy-5xy)/(5xy+2xy)

=5/7

1/x+1/y=5
左边通分。。。
(x+y)/(xy)=5
x+y=5xy

(2X-5XY+2Y)/(X+2XY+Y)
=[2(x+y)-5xy]/[(x+y)+2xy]
=(10xy-5xy)/(5xy+2xy)
=(5xy)/(7xy)
=5/7

因为 1/x+1/y=5
所以（x+y）/xy=5
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

X+Y/XY=5
(2X-5XY+2Y)/(X+2XY+Y)
(5XY)/(7XY)=5/7

由1/x+1/y=5,
得，x+y=5xy
所以(2x-5xy+2y)/(x+2xy+y)
=[2（x+y）-5xy]/[(x+y)+2xy]
=(10xy-5xy)/(5xy+2xy)
=5/7