The image provides the following problem:

Determine the domain of the function $f(x) = \frac{x^2 + 4x + 5}{x^2 - 25}$.

To find the domain, we need to identify the values of $x$ that would make the denominator zero, since division by zero is undefined.

The denominator is $x^2 - 25$, which can be factored as: $x^2 - 25 = (x - 5)(x + 5)$ Thus, the function will be undefined when: $x - 5 = 0 \quad \text{or} \quad x + 5 = 0$ This gives $x = 5$ and $x = -5$.

Therefore, the domain excludes $x = 5$ and $x = -5$, which can be written in interval notation as: $(-\infty, -5) \cup (-5, 5) \cup (5, \infty)$

The correct answer is:

D) $(-\infty, -5) \cup (-5, 5) \cup (5, \infty)$

Would you like more details on this, or have any questions?

Here are five related questions:

1. How do we determine the domain of a rational function?
2. What happens when the denominator of a function equals zero?
3. Can a function have more than two discontinuities in its domain?
4. How can factoring help find the domain of a function?
5. How do you represent domains using interval notation?

Tip: Always check for points where the denominator of a rational function is zero to find restrictions on the domain.