∵ ,x^2+9y^2-8xy=0,∴ (x+3y)^2=14xy,(x-3y)^2=2xy,∴(x+3y)^2/(x-3y)^2=14/2=7,
∵ y＞x＞0,∴x-3y＜0,∴(x+3y)/(x-3y)= -√7 .