If c (x) = 5/x-2 and d (x) = x+3 what is the domain of (cd) (x) ?

First you must realize that the domain is restricted for c (x), in that division by zero is undefined, so x cannot equal 2. Realizing this before you start is important because the final form of (cd) (x) may appear to not have that restriction, but having x=2, would still have no meaning regardless of what (cd) (x) becomes.

(cd) (x) = 5 (x+3) / (x-2)

(cd) (x) = (5x+15) / (x-2)

Now we can see that the same restriction applies to the composite function, so the domain is: x = (-oo, 2) U (2, + oo). "All real numbers except two."