Restrictions on Variables of Logs

Hi there

I just have a quick question regarding this question:

Simplify. State any restrictions on the variables.

log(x^2+7x+12)-log(x^2-9)

my answer is log[(x+4)/(x-3)] which is correct. However, for the restrictions, I believe that they are: x>3 and x<-4.. But the back of the book says only x>3.

When I plug in x<-4 any number such as x=-5 the expression is defined. So.. my question, is the back of the book wrong? Are there 2 restrictions and not one?

Thanks, please explain your answer fully.