数学题,分式,急!

来源:百度知道 编辑:UC知道 时间:2024/06/03 16:47:02
已知,x-3y=0,求〔(2x+y)/(x^2)-2xy+(y^2)〕*(x-y)的值

按我以前的经验,你写的题应该是这样的
x-3y=0
x=3y

{(2x+y)/[(x^2)-2xy+(y^2)]}*(x-y)
={(2*3y+y)/[(x^2)-2*3y*y+y^2]}*(3y-y)
=[7y/(x^2-5y^2)]*2y
={7y/[(3y)^2-5y^2]}*2y
=[7y/(9y^2-5y^2)]*2y
=(7y/4y^2)*2y
=7/2

x-3y=0
x=3y

〔(2x+y)/(x^2)-2xy+(y^2)〕*(x-y)
={(2*3y+y)/(x^2)-2*3y*y+y^2}*(3y-y)这步其实可以不用写,怕你看不明白
=(7y/x^2-5y^2)*2y因式化简
=(7y/x^2-5y^2)*2y
=7y/9y^2*2y-5y^2*2y
=14y/9y-10y^3
=14/9y-10y^3

x=3y代入
〔(2x+y)/(x^2)-2xy+(y^2)〕*(x-y)
=[7y/(9y^2)-6Y^2+y^2]*2Y
=14/9-10y^3