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The image shows a problem that involves finding the domain of two rational functions. Let’s analyze and solve the problem step-by-step:

### Given Functions
1. \( f(x) = \frac{x^2}{x^2 - 9} \)
2. \( g(x) = \frac{x}{x - 3} \)

### Domain of a Function
The domain of a function includes all real numbers except where the function is undefined. For rational functions, these points occur where the denominator is zero.

### Step-by-step Solutions

#### 1. Domain of \( f(x) = \frac{x^2}{x^2 - 9} \)
- The denominator is \(x^2 - 9\).
- Set the denominator equal to zero:  
  \[
  x^2 - 9 = 0
  \]
  \[
  x^2 = 9
  \]
  \[
  x = \pm 3
  \]
- Therefore, the function \( f(x) \) is undefined at \( x = 3 \) and \( x = -3 \).

**Domain of \( f(x) \):** All real numbers except \( x = 3 \) and \( x = -3 \).  
In interval notation: \( (-\infty, -3) \cup (-3, 3) \cup (3, \infty) \).

#### 2. Domain of \( g(x) = \frac{x}{x - 3} \)
- The denominator is \(x - 3\).
- Set the denominator equal to zero:  
  \[
  x - 3 = 0
  \]
  \[
  x = 3
  \]
- Therefore, the function \( g(x) \) is undefined at \( x = 3 \).

**Domain of \( g(x) \):** All real numbers except \( x = 3 \).  
In interval notation: \( (-\infty, 3) \cup (3, \infty) \).

### Conclusion
- **Domain of \( f(x) \):** \( (-\infty, -3) \cup (-3, 3) \cup (3, \infty) \)
- **Domain of \( g(x) \):** \( (-\infty, 3) \cup (3, \infty) \)

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### Related Questions to Explore:
1. How do you find the domain of a function with both a numerator and denominator that are polynomials?
2. What happens to the graph of a function at points where it is undefined?
3. How do you find the range of a rational function?
4. What is the difference between a vertical asymptote and a hole in the graph of a function?
5. How does the concept of limits help in understanding points where a function is undefined?

### Tip
When determining the domain of a rational function, always identify the values that make the denominator zero and exclude them from the domain.

Find the domain of the following rational functions: f(x) = x^2 / (x^2 - 9) and g(x) = x / (x - 3)

Explore the step-by-step process to find the domain of rational functions. This problem focuses on the rational functions f(x) = x^2 / (x^2 - 9) and g(x) = x / (x - 3), covering the algebraic concepts needed to determine where each function is undefined.

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