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The image contains a mathematical expression. Here is what it looks like:

Given:
\[ f(x) = \frac{(x - 1) \times (x - 2)}{(x - 1) \times (x - 3)} \]

You need to simplify this expression.

### Simplification:

1. First, observe that the numerator and the denominator both contain the factor \((x - 1)\).

2. Since \((x - 1)\) is common in both numerator and denominator, they can cancel each other out (as long as \(x \neq 1\) because the expression is undefined for \(x = 1\)).

   Thus, the simplified expression is:
   \[
   f(x) = \frac{x - 2}{x - 3}
   \]

However, this simplification assumes that \(x \neq 1\), because at \(x = 1\), the original function is undefined.

### Final Answer:
\[
f(x) = \frac{x - 2}{x - 3}
\]
with the domain restrictions \(x \neq 1\) and \(x \neq 3\) (since \(x = 3\) would make the denominator zero).

Do you need further details or have any other questions?

### Related Questions:
1. How do you determine the domain of a rational function?
2. What happens if you cancel out a factor from both the numerator and the denominator?
3. What is the behavior of the function near points where the expression is undefined?
4. How would you graph the simplified function \(\frac{x - 2}{x - 3}\)?
5. How does the simplification process change if there's no common factor in both the numerator and denominator?

### Tip:
Always check for domain restrictions when simplifying rational expressions to avoid mistakenly assuming the function is defined where it actually isn’t.

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Learn how to simplify the rational function f(x) = (x - 1) × (x - 2) / ((x - 1) × (x - 3)) by canceling common factors and understanding domain restrictions. Suitable for students in Grades 9-10.

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