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To create a complex fraction that has excluded values \( x \neq -2 \) and \( x \neq 5 \), the denominator should contain factors that would make the fraction undefined at these values. Specifically, the terms \( (x + 2) \) and \( (x - 5) \) should appear in the denominator since these would make the denominator zero when \( x = -2 \) and \( x = 5 \), respectively.

Here's an example of such a complex fraction:

\[
\frac{\frac{2x}{x+1}}{\frac{x^2 - 4}{(x + 2)(x - 5)}}
\]

In this fraction:
- The numerator is \( \frac{2x}{x+1} \).
- The denominator is \( \frac{x^2 - 4}{(x + 2)(x - 5)} \).
  
This fraction is undefined for \( x = -2 \) and \( x = 5 \) due to the terms in the denominator.

Would you like more details or have any questions about this?

Here are five follow-up questions you could explore:
1. What other values of \( x \) could make this complex fraction undefined?
2. How can this complex fraction be simplified?
3. How do you find the excluded values of any fraction?
4. What happens to the graph of the function when \( x = -2 \) or \( x = 5 \)?
5. Can you create a different complex fraction with the same excluded values?

**Tip:** Always check the denominator of a fraction for values that make it zero, as these will be the excluded values.

Make up a complex fraction that has excluded values x ≠ -2 and x ≠ 5.

Explore how to create a complex fraction with excluded values x ≠ -2 and x ≠ 5. Understand how factors in the denominator lead to these restrictions in algebraic expressions, suitable for high school students learning algebra.

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