To find the domain of the expression \( \frac{x}{x - 3} \), we need to determine the values of \( x \) for which the expression is defined.

The key restriction in a rational expression is that the denominator cannot be zero because division by zero is undefined.

### Step-by-Step Process:
1. **Identify the denominator**: The denominator is \( x - 3 \).
2. **Set the denominator not equal to zero**: 
   \[
   x - 3 \neq 0
   \]
3. **Solve for \( x \)**: 
   \[
   x \neq 3
   \]
   
Thus, the expression is undefined when \( x = 3 \).

### Conclusion:
The domain of \( \frac{x}{x - 3} \) is all real numbers except \( x = 3 \). In interval notation, this is:
\[
(-\infty, 3) \cup (3, +\infty)
\]

Would you like more details or further explanations?

Here are 5 related questions:
1. What is the range of \( \frac{x}{x - 3} \)?
2. How do you find the vertical asymptote of \( \frac{x}{x - 3} \)?
3. Can you simplify the expression further?
4. What happens to the value of \( \frac{x}{x - 3} \) as \( x \to 3 \)?
5. What are other common types of discontinuities in rational functions?

**Tip**: Always check for restrictions on the domain when dealing with rational functions by examining the denominator.

Learn how to find the domain of the rational function x/(x-3). This solution explains why the denominator cannot be zero and walks through the process of determining the domain, which excludes x = 3. Suitable for students in Grades 8-10.

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