Answer
$\color{blue}{(-\infty, 0.25) \cup (0.25, 3) \cup (3, +\infty)}$
Work Step by Step
Find the domain of each function:
For $f(x)$, the value of $x$ can be any real number except 3 since it will make the denominator zero, which is not allowed.
Thus, domain of $f(x)$ is $(-\infty, 3) \cup (3, +\infty)$
For $f(x)$, the value of $x$ can be any real number except $0.25$ since it will make the denominator zero, which is not allowed.
Thus, domain of $f(x)$ is $(-\infty, 0.25) \cup (0.25, +\infty)$
RECALL:
The domain of the sum, difference, and product of $f(x)$ and $g(x)$ is the common elements of the domains of the two functions.
Note that:
$[(-\infty, 3) \cup(3, +\infty)] \cap [(-\infty, 0.25) \cup (0.25, +\infty)]
\\= (-\infty, 0.25) \cup (0.25, 3) \cup (3, +\infty)$.
Thus, the domain of the sum, difference, and product of $f(x)$ and $g(x)$ is:
$\color{blue}{(-\infty, 0.25) \cup (0.25, 3) \cup (3, +\infty)}$
