To evaluate the limit:

\[
\lim_{{x \to 9}} \frac{9 - x}{x - 3}
\]

Substitute \( x = 9 \) directly into the expression:

\[
\frac{9 - 9}{9 - 3} = \frac{0}{6} = 0
\]

Thus, the limit is:

\[
\boxed{0}
\]

Would you like a more detailed explanation or have any questions?

Here are some related questions:
1. What is a limit, and how do we calculate it for more complex functions?
2. How does substitution work when evaluating limits?
3. What happens if direct substitution results in an indeterminate form (e.g., \( \frac{0}{0} \))?
4. What are one-sided limits, and how are they useful?
5. How does continuity of a function affect the calculation of limits?

**Tip:** Always try direct substitution first when evaluating a limit. If it leads to an indeterminate form, then consider using algebraic simplification, factoring, or L'Hôpital's rule.

Learn how to evaluate the limit of (9-x)/(x-3) as x approaches 9 using direct substitution. This solution covers the concept of limits, substitution, and continuity. Suitable for Grades 11-12 calculus students.

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