已知x^2+xy-6y^2=0,且y不等于0 .求：（1）x\y的值（2）x+3y\x-3y的值

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$已知x^2+xy-6y^2=0,且y不等于0 .求：（1）x\y的值（2）x+3y\x-3y的值$

x^2+xy-6y^2=0
x^2-4y^2+xy-2y^2=0
(x+2y)(x-2y)+y(x-2y)=0
(x-2y)(x+2y+y)=0
(x-2y)(x+3y)=0
x-2y=0
x+3y=0
x/y=2
x/y=-3
x\y的值为2或-3
当x=2y时
(x+3y)/(x-3y)=(2y+3y)/(2y-3y)=5y/(-y)=-5
当x=-3y时
(x+3y)/(x-3y)=(-3y+3y)/(-3y-3y)=0
(x+3y)/(x-3y)的值为-5或0

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