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

For rational functions like this one, the function is undefined where the denominator is zero. So, we need to find where \( 5 - x = 0 \).

1. Set the denominator equal to zero:
   \[
   5 - x = 0
   \]

2. Solve for \( x \):
   \[
   x = 5
   \]

Thus, the function is undefined at \( x = 5 \). Therefore, the domain of \( f(x) \) is all real numbers except \( x = 5 \).

**Final answer**: The domain of the function is \( (-\infty, 5) \cup (5, \infty) \).

Would you like further details, or do you have any questions? Here are 5 related questions for practice:

1. What is the domain of \( f(x) = \frac{1}{x-3} \)?
2. How do you find the domain of \( f(x) = \frac{2x + 1}{x^2 - 4} \)?
3. What happens to a function if its denominator is zero at a certain point?
4. Can you explain the concept of undefined points in rational functions?
5. What would the domain be for \( f(x) = \frac{x + 1}{x^2 + x - 6} \)?

**Tip**: Always check the denominator for zeros when finding the domain of a rational function!

Find the domain of the function f(x) = (x + 2) / (5 - x).

Learn how to find the domain of the rational function f(x) = (x + 2) / (5 - x). This problem involves analyzing rational functions and finding where the function is undefined. Suitable for Grades 9-11 students learning algebraic concepts.

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