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To determine the x-intercepts of the rational function \( h(x) = \frac{x^2 - 9}{x^2 - 4} \), we need to find the values of \( x \) where \( h(x) = 0 \). 

1. **Set the numerator equal to zero**:
\[ x^2 - 9 = 0 \]

2. **Solve for \( x \)**:
\[ x^2 = 9 \]
\[ x = \pm 3 \]

3. **Check if these values make the denominator zero**:
\[ x^2 - 4 = 0 \]
\[ x^2 = 4 \]
\[ x = \pm 2 \]

Since \( x = \pm 2 \) makes the denominator zero, these values are vertical asymptotes and not x-intercepts.

4. **Verify \( x = 3 \) and \( x = -3 \)**:
   - For \( x = 3 \):
     \[ h(3) = \frac{3^2 - 9}{3^2 - 4} = \frac{9 - 9}{9 - 4} = \frac{0}{5} = 0 \]
   - For \( x = -3 \):
     \[ h(-3) = \frac{(-3)^2 - 9}{(-3)^2 - 4} = \frac{9 - 9}{9 - 4} = \frac{0}{5} = 0 \]

Therefore, \( x = 3 \) and \( x = -3 \) are valid x-intercepts.

**Summary:**

- The rational function \( h(x) = \frac{x^2 - 9}{x^2 - 4} \) has x-intercepts at both \( x = 3 \) and \( x = -3 \).

So, the correct answer is:

\[ \boxed{\text{iii) Both I and II}} \]

**Do you want details or have any questions?**

Here are 8 related questions for further understanding:
1. What are the vertical asymptotes of the function \( h(x) = \frac{x^2 - 9}{x^2 - 4} \)?
2. How do you determine the horizontal asymptotes of a rational function?
3. What is the behavior of the function \( h(x) = \frac{x^2 - 9}{x^2 - 4} \) near the vertical asymptotes?
4. How do you simplify the expression \( h(x) = \frac{x^2 - 9}{x^2 - 4} \)?
5. What is the difference between a hole and a vertical asymptote in a rational function?
6. How do you find the y-intercept of the function \( h(x) = \frac{x^2 - 9}{x^2 - 4} \)?
7. What is the significance of the x-intercepts in the graph of a rational function?
8. How do you graph the function \( h(x) = \frac{x^2 - 9}{x^2 - 4} \)?

**Tip:** Always factor both the numerator and the denominator completely to identify any common factors that might indicate a hole in the graph.

Learn how to find the x-intercepts of the rational function h(x) = (x^2 - 9) / (x^2 - 4) with a detailed step-by-step solution. Understand the concept of rational functions, vertical asymptotes, and graphing techniques. Suitable for high school students.

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