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We are given the function:

\[
h(x) = \frac{x^2 + 5x - 24}{x^2 - 81}
\]

We need to find \( h(-9) \).

Let's substitute \( x = -9 \) into the function and simplify:

1. First, simplify the numerator:
   \[
   (-9)^2 + 5(-9) - 24 = 81 - 45 - 24 = 12
   \]
   
2. Now simplify the denominator:
   \[
   (-9)^2 - 81 = 81 - 81 = 0
   \]

Since the denominator is 0, the function is undefined at \( x = -9 \).

Therefore, \( h(-9) \) **is not defined**.

Would you like further details or have any questions?

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Here are 5 related questions:

1. What conditions make a rational function undefined?
2. How can we factor the denominator \(x^2 - 81\)?
3. Could there be other points where the function is undefined?
4. How would you analyze a similar function if the denominator didn't result in zero?
5. How does the vertical asymptote relate to this function being undefined?

**Tip:** Always check the denominator for zeros when evaluating a rational function to determine where it might be undefined.

La función h está definida a continuación: h(x) = (x^2 + 5x - 24) / (x^2 - 81). Hallar h(-9).

Learn how to evaluate the rational function h(x) = (x^2 + 5x - 24) / (x^2 - 81) by substituting x = -9. This problem involves simplifying expressions and checking when a function becomes undefined due to division by zero.

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