The domain of the quotient between the two functions is the intersection of the domain of each individual function, except the points where g(x)=0.
In any case, the denominator must be different from 0.
The domain of f is the set of all real numbers except x=-2, since:
[tex]x=-2\Rightarrow-x-2=-(-2)-2=2-2=0[/tex]
The domain of g is the set of all real numbers except x=-4. This can be proven using a similar procedure.
On the other hand, g(x)=0 whenever x=4.
Therefore, the domain of f(x)/g(x) is the set of all real numbers, except:
[tex]\begin{gathered} x=-2 \\ x=4 \\ x=-4 \end{gathered}[/tex]
