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Answer
The expression \( \frac{x}{x-3} \) is undefined when \( x = 3 \).
Solution
1. For the expression \( \frac{x}{x-3} \) to be defined, the denominator cannot be zero.
2. Set the denominator equal to zero:
\[
x - 3 = 0
\]
3. Solve for \( x \):
\[
x = 3
\]
4. Therefore, the expression is undefined when \( x = 3 \).
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The expression \( \frac{x}{x-3} \) becomes undefined when the denominator equals zero. This happens when \( x - 3 = 0 \), so solving for \( x \), we find that \( x = 3 \). Thus, the expression is undefined at this specific value, leading to a potential discontinuity in any graph or analysis involving this fraction. It's always a good idea to check for other values that might lead to undefined scenarios in more complex expressions. For instance, every time you're dealing with fractions, keep an eye on the denominator! If it equals zero, you know you have a no-go zone for values of \( x \) that would make your math go haywire.
