Composite Function Domain will include infinity or not in the below case

Question

Consider the function h(x) = $f(g(x)) = \frac{3}{\frac{6}{3-x}}$ from $g(x) = \frac{6}{3-x}$ and $f(x) = \frac{3}{x}$ , we will say that h(x) to be not defined at infinity and -infinity as both those points make the denomiator of h(x) to be zero ? So there will be three points where h(x) is not defined at $\infty , - \infty$ and $3 $? Or does the set of real numbers always exclude the infinity points so we dont take it into conideration ?