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To find the domain of the function \( f(x) = \frac{5}{x-6} + \frac{1}{x-8} \), we need to determine when the function is undefined. This will happen when any denominator is zero because division by zero is not allowed.

### Steps:

1. **Identify the denominators**: The denominators are \( x - 6 \) and \( x - 8 \).
   
2. **Set each denominator equal to zero** and solve for \( x \):
   - \( x - 6 = 0 \) ⟹ \( x = 6 \)
   - \( x - 8 = 0 \) ⟹ \( x = 8 \)

3. **Determine the restrictions**: The function is undefined when \( x = 6 \) and \( x = 8 \). Therefore, the domain excludes these two values.

### Domain:
The domain of \( f(x) \) is all real numbers except \( x = 6 \) and \( x = 8 \). In interval notation, this is:

\[
(-\infty, 6) \cup (6, 8) \cup (8, \infty)
\]

Would you like any further clarification?

Here are some related questions you might find useful:

1. How do we find the domain of a rational function in general?
2. What happens to the graph of \( f(x) \) at \( x = 6 \) and \( x = 8 \)?
3. How do vertical asymptotes relate to the domain of a function?
4. Can we simplify the function \( f(x) \) in any way before analyzing its domain?
5. How would the domain change if we added or subtracted constants from the denominators?

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

Find the domain of the function f(x) = 5/(x-6) + 1/(x-8).

Learn how to find the domain of the rational function f(x) = 5/(x-6) + 1/(x-8). This solution involves understanding restrictions on denominators and avoiding division by zero. Suitable for students in Grades 9-11.

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