Hi there

I need help with the restrictions on the variables of this question:

Simplify. State any restrictions on the variables.

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

So my answer is: log(x+4/x-3) which is correct.

Now for the restrictions, I have:

x<-4 and x>3

However the back of the book says the answer is only x>3 and not x<-4 for the restrictions of the variables. But when I sub in any number such as -5 into the ORIGINAL log equation, i get a defined and positive log of x value. So? is mine correct or theirs? Explain fully.