Answer
The domain of $H(x)$ is the set of all real numbers.
Work Step by Step
Rational functions are of the form
$$R(x)=\dfrac{p(x)}{q(x)}$$
The domain of the rational function is the set of all real numbers except those for which the denominator $q(x)$ is $0$
$\text{Setting the denominator equal to zero}$
$$x^2+4=0\\[3mm]\\
x^2=-4 \\
\text{ This has no real roots because when a real number is squared, the result is never a negative number.}$$
Thus, the domain of $H(x)$ is the set of all real numbers.
