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The given expression is:

\[
\frac{x - 3}{(x - 14)(x - 3)}
\]

To simplify this expression, notice that \(x - 3\) is a common factor in both the numerator and the denominator. Thus, we can cancel out the \(x - 3\) term from both:

1. **Simplification**: 

   \[
   \frac{x - 3}{(x - 14)(x - 3)} = \frac{1}{x - 14} \quad \text{for } x \neq 3
   \]

   It's important to note that the expression is undefined when \(x = 3\) because it results in division by zero.

2. **Domain**: 

   The simplified form is \(\frac{1}{x - 14}\), but the original function has restrictions:
   - \(x \neq 3\) because the original denominator \((x - 3)\) would be zero.
   - \(x \neq 14\) because \((x - 14)\) would also be zero.

   So, the domain of the function is all real numbers except \(x = 3\) and \(x = 14\).

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

### Related Questions:
1. What are the values of \(x\) for which the original expression is undefined?
2. How can you find vertical asymptotes of a rational function like this?
3. How does cancelling terms affect the graph of the function?
4. Can the cancelled term affect the behavior of the graph at a particular point?
5. How do you determine holes in the graph of a rational function?

**Tip:** Always check the domain of a function after simplifying to ensure you haven't lost any important information about where the function is defined.

Simplify the expression \( \frac{x - 3}{(x - 14)(x - 3)} \).

Learn how to simplify the rational expression (x - 3) / ((x - 14)(x - 3)) by canceling common factors. This problem highlights key algebraic concepts, including the simplification of rational expressions and determining the domain. Suitable for students in Grades 9-11.

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