Mathematics

Problem

Two rational functions are defined as

f(x)=\frac{2x+1}{x^{2}-4},\quad g(x)=\frac{x-3}{x^{2}-9}.

Let

h(x)=f(x)+g(x).

Answer the following. (a) Determine the domain of

f

. (b) Determine the domain of

g

. (c) Using your results from parts (a) and (b), obtain the domain of

h

, showing all steps and justifying every exclusion.