/sci/ - Science & Math

I have a question about combined functions.
I have f(x)=2/x and g(x)=4/(x+4)
I know the domains of these, are x=/=0 and x=/=-4
I know if i added these functions and checked the restrictions on would get a combined domain. But when I divide these functions (f/g)(x), (2/x)/(4/x+4) I get (x+4)/2x which evaluated independently the domain would be (-infinity, 0)U(0, infinity) however, the solution posted includes the -4 as a restriction, denominator only have 0 as a restriction. Why is that?