f(x^2-3)=logx^2/(x^2-6)
=log(x^2-3+3)/(x^2-3-3)
所以f(x)=log(x+3)/(x-3)
真数大于0
(x+3)/(x-3)>0
(x+3)(x-3)>0
x<-3,x>3
所以定义域
(-∞,-3)∪(3,+∞)