To find the domain of the rational function \( h(x) = \frac{x + 8}{x^2 - 64} \), we need to identify the values of \( x \) that will make the denominator zero, as these will be the values that are not allowed in the domain.
First, set the denominator equal to zero:
\[ x^2 - 64 = 0 \]
Next, solve for \( x \):
\[ x^2 = 64 \] \[ x = \pm 8 \]
The values \( x = 8 \) and \( x = -8 \) will make the denominator zero. Therefore, these values need to be excluded from the domain.
Thus, the domain of \( h(x) \) in interval notation will be:
\[ (-\infty, -8) \cup (-8, 8) \cup (8, \infty) \]
Now we can complete the choice:
A. The domain of \( h(x) \) is restricted to \((- \infty, -8) \cup (-8, 8) \cup (8, \infty)\).