To find the domain of the function $f(x) = \frac{x + 5}{2 - x}$, we need to determine for which values of $x$ the function is defined.

Since division by zero is undefined, we must ensure that the denominator of the function is not zero. The denominator is $2 - x$, so we need to solve the equation:

$2 - x \neq 0$

Solving for $x$:

$x \neq 2$

Thus, the function is undefined at $x = 2$. Therefore, the domain of $f(x)$ is all real numbers except $x = 2$.

In interval notation, the domain is:

$(-\infty, 2) \cup (2, \infty)$

Would you like more details or have any further questions?

Here are 5 related questions to expand on this:

1. How does the domain of a rational function change if the numerator is also zero?
2. What happens to the graph of the function near $x = 2$?
3. Can we simplify the function in any special cases?
4. What is the range of the function $f(x) = \frac{x + 5}{2 - x}$?
5. How would the domain change if there were a square root involved in the function?

Tip: Always check for values that make the denominator zero when finding the domain of rational functions.