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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.

Determine the domain of the function f(x) = (x^2 + 4x + 5) / (x^2 - 25).

Explore how to determine the domain of the function f(x) = (x^2 + 4x + 5) / (x^2 - 25), including a step-by-step guide on factorizing the denominator and identifying values that make the function undefined.

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