ok, so i came accross this problem

(don't know how to subscript here...4 is the base)

g(x) = log4((x+3)/x)

and i have to find the domain. now, i know that (x+3)/x has to be greater than 0, and obviously, x cannot equal 0. i also know that the domain is negative infinity to -3 and 0 to positive infinity because at x<-3, we would have a negative divided by a negative which would yield a positive number and at -3<x<=0 it would be a negative number (or 0 which we don't want). i can see all this. it is obvious. but my problem is working this out on paper.

i know that on the denominator x > 0, but when i work out the top, x+3>0 goes to x>-3 is what i get. so that says that x>-3 and x>0...

this doesn't show that the domain is (-infinity, -3) U (0, infinity)...so how do i work that out on paper. I know this will kill me on more complex equations if i don't figure this out.

I would sincerely appreciate any help figuring this out . I would also like to apologize if I posted incorrectly in anyway (this is my first post).