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To solve the given subtraction of fractions, we first identify a common denominator. The expressions \( x - 4 \) and \( 3x - 12 \) can be used for this purpose. Note that \( 3x - 12 \) can be factored further into \( 3(x - 4) \).

### Steps to Solve:

1. **Identify the Least Common Denominator (LCD)**: The LCD for \( x - 4 \) and \( 3(x - 4) \) is \( 3(x - 4) \).
2. **Rewrite each fraction with the LCD as the denominator**:
   - For \( \frac{x}{x-4} \), multiply numerator and denominator by 3: \( \frac{x \cdot 3}{(x-4) \cdot 3} = \frac{3x}{3(x-4)} \)
   - \( \frac{2}{3x-12} \) already has the denominator \( 3(x-4) \), so it remains \( \frac{2}{3(x-4)} \).
3. **Perform the subtraction**:
   - \( \frac{3x}{3(x-4)} - \frac{2}{3(x-4)} = \frac{3x - 2}{3(x-4)} \)

The result of the subtraction is \( \frac{3x - 2}{3(x-4)} \).

### Answer:
\[ \frac{3x - 2}{3(x-4)} \]

Would you like more details on any step or have any questions about this problem? Here are some related questions:

1. How would you find the common denominator for a different pair of expressions?
2. What would be the steps to add fractions instead of subtracting?
3. Can you solve for \( x \) when \( \frac{3x - 2}{3(x-4)} = 0 \)?
4. What are the restrictions on the value of \( x \) in this expression?
5. How would this problem change if the numerator of the second fraction was different?

**Tip**: Always factor expressions completely when looking for a common denominator to simplify the handling of terms.

Subtract. \( \frac{x}{x-4} - \frac{2}{3x-12} \)

Learn how to subtract algebraic fractions with a detailed solution for \( \frac{x}{x-4} - \frac{2}{3x-12} \). This problem covers key algebra concepts such as factoring and finding a common denominator, ideal for students in Grades 9-11.

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