已知x2-7xy+12y2=0(y≠0),求(x-y)/(x+2y)的值

已知x2-7xy+12y2=0(y≠0),求(x-y)/(x+2y)的值
已知x2-7xy+12y2=0(y≠0),求(x-y)/(x+2y)的值

已知x2-7xy+12y2=0(y≠0),求(x-y)/(x+2y)的值
x²-7xy+12y²=0
(x-3y)(x-4y)=0
x=3y或x=4y
x=3y时,
(x-y)/(x+2y)=(3y-y)/(3y+2y)=(2y)/(5y)=2/5
x=4y时,
(x-y)/(x+2y)=(4y-y)/(4y+2y)=(3y)/(6y)=1/2

分解因式得（x-3y)(x-4y)=0
x-3y=0或x-4y=0
x=3y或x=4y
当x=3y时,x-y/x+2y=3y-y/3y+2y=2/5
当x=4y时,x-y/x+2y=4y-y/4y+2y=1/2

x2-7xy+12y2=0(y≠0)
(x-3y)(x-4y)=9
所以x=3y或x=4y
所以(x-y)/(x+2y)=2y/(5y)=2/5或(x-y)/(x+2y)=3y/(6y)=1/2

x^2-7xy+12y^2=0(y≠0)
(x-3y)(x-4y)=0(y≠0)
x=3y或x=4y(y≠0)
所以，当x=3y(y≠0)，（x-y)／(x+2y)=2／5
当x=4y(y≠0)，（x-y)／(x+2y)=1／2
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