x^2-2xy-3y^2=0,求(x+2y)/(x-y)的值

x^2-2xy-3y^2=(x+y)(x-3y)=0，所以有x=-y或x=3y
当x=-y时，(x+2y)/(x-y)=y/(-2y)=-1/2
当x=3y时，(x+2y)/(x-y)=5y/2y=5/2

(x+2y)/(x-y)=1+3y/(x-y)------1
由x^2-2xy-3y^2=0
可得（x-y)^2-y^2-3y^2=0
(x-y)^2=4y^2
x-y=2y或x-y=-2y
代入1式
得(x+2y)/(x-y)=5/2或(x+2y)/(x-y）=-1/2