Suppose that $$f(x) = \frac{1}{x-3} \quad \mathrm{and} \quad g(x) = \frac{x-5}{x+2}.$$ For each function $h$ given below, find a formula for $h(x)$ and the domain of $h$. Use interval notation for entering the domains.

(A) $h(x) = (f \circ g)(x)$.

$h(x)$ =
Domain =

(B) $h(x) = (g \circ f)(x)$.

$h(x)$ =
Domain =

(C) $h(x) = (f \circ f)(x)$.

$h(x)$ =
Domain =

(D) $h(x) = (g \circ g)(x)$.

$h(x)$ =
Domain =