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To find the domain of the function:

\[
f(x) = \frac{3}{x - 11} + \frac{4}{x + 3}
\]

we need to determine where the function is undefined. A rational function like this is undefined when the denominator of any term is zero because division by zero is not allowed.

### Step-by-step:
1. The first term is \(\frac{3}{x - 11}\). The denominator \(x - 11\) becomes zero when \(x = 11\).
2. The second term is \(\frac{4}{x + 3}\). The denominator \(x + 3\) becomes zero when \(x = -3\).

### Conclusion:
The function is undefined at \(x = 11\) and \(x = -3\).

### Domain:
The domain of the function is all real numbers except \(x = 11\) and \(x = -3\).

In interval notation, the domain is:
\[
(-\infty, -3) \cup (-3, 11) \cup (11, \infty)
\]

Would you like more details or have any questions?

Here are five related questions:
1. How do you find the domain of more complex rational functions?
2. What happens to the graph of a function at points where it is undefined?
3. How do vertical asymptotes relate to the domain of a rational function?
4. Can a function have more than two points where it is undefined?
5. How would the domain change if a square root or logarithmic term was added?

**Tip:** Always check for zeroes in the denominator when determining the domain of rational functions.

Find the domain of the function: f(x) = 3/(x - 11) + 4/(x + 3)

Learn how to find the domain of the rational function f(x) = 3/(x - 11) + 4/(x + 3). This problem involves understanding rational functions and identifying points where the function is undefined. Suitable for students in Grades 9-11.

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