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.