To find the domain of the function $f(x) = \frac{x + 6}{5 - x}$, we need to determine when the function is defined. The only restriction in this function comes from the denominator, as division by zero is undefined.

1. Set the denominator equal to zero to find where the function is undefined: $5 - x = 0$ Solving for $x$: $x = 5$

2. Since the denominator cannot be zero, the function is undefined at $x = 5$.

Therefore, the domain of the function is all real numbers except $x = 5$.

Domain: $x \in (-\infty, 5) \cup (5, \infty)$

Would you like more details or have any further questions?

Here are some related questions:

1. How do you find the domain of a function with multiple restrictions?
2. What is the difference between the domain and the range of a function?
3. How does the domain change if the function has a square root?
4. Can the domain of a rational function be a set of discrete values?
5. What happens to the graph of the function near $x = 5$?

Tip: Always check the denominator of a rational function to ensure you're not dividing by zero!