The expression \(\frac{6x - 5}{4x - 12}\) can be simplified. Let's break it down:

### Step 1: Factor the denominator.
The denominator \(4x - 12\) can be factored as follows:
\[
4x - 12 = 4(x - 3)
\]
So, the expression becomes:
\[
\frac{6x - 5}{4(x - 3)}
\]

### Step 2: Simplify the expression.
At this point, there is no common factor between the numerator and the denominator, so the expression cannot be simplified further. Therefore, the simplified form of the expression is:
\[
\frac{6x - 5}{4(x - 3)}
\]

Would you like details or have any questions?

Here are 5 questions to expand your understanding:
1. How do you factor a polynomial like \(4x - 12\)?
2. What does it mean to simplify an algebraic expression?
3. How can you identify common factors in a fraction?
4. Why can't the expression \(\frac{6x - 5}{4(x - 3)}\) be simplified further?
5. How would you solve the equation if \(\frac{6x - 5}{4(x - 3)} = 0\)?

**Tip:** Always check for common factors in the numerator and denominator when simplifying algebraic expressions.

Learn how to simplify the rational expression (6x - 5) / (4x - 12) step-by-step with detailed explanations. This problem covers key algebraic concepts such as rational expressions and factoring. Suitable for high school students.

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