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The given function is:

\[
f(x) = \frac{x - 3}{2x - 5}
\]

To find what number must be excluded from the domain of \( f \), we need to determine when the denominator becomes zero, as division by zero is undefined in mathematics.

The denominator is \( 2x - 5 \). Set this equal to zero and solve for \( x \):

\[
2x - 5 = 0
\]

\[
2x = 5
\]

\[
x = \frac{5}{2}
\]

So, \( x = \frac{5}{2} \) must be excluded from the domain because it would make the denominator zero, which is undefined.

### Answer:
The number that must be excluded from the domain is \( x = \frac{5}{2} \).

Would you like any further details on this or have any other questions?

Here are 5 related questions you might explore:
1. What is the domain of \( f(x) \) excluding the value \( x = \frac{5}{2} \)?
2. How does the behavior of the function change near \( x = \frac{5}{2} \)?
3. Can you express the function's behavior as \( x \to \frac{5}{2} \) from the left and right?
4. What happens to \( f(x) \) when \( x = 0 \)?
5. How can you graph this rational function and mark its vertical asymptote?

**Tip**: When working with rational functions, always check for values that make the denominator zero, as these values need to be excluded from the domain.

Work out what number must be excluded from the domain of f(x) = (x - 3) / (2x - 5).

Learn how to exclude values from the domain of the rational function f(x) = (x - 3) / (2x - 5). This example illustrates how to find when the denominator becomes zero, which makes the function undefined. Suitable for students in Grades 9-12.

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