For $f(x) = \frac{x}{x-3}$ and $g(x) = -\frac{8}{x}$, find the following composite functions and state the domain of each:
A$f \circ g$
B$g \circ f$
C$f \circ f$
D$g \circ g$
A$f \circ g$
B$g \circ f$
C$f \circ f$
D$g \circ g$