https://file.aiquickdraw.com/mathbot/file/1725520914639c0sv8c7l.jpg

The image asks to simplify the following expression:

\[
\frac{\frac{x - 6}{3}}{\frac{4x - 24}{x - 3}}
\]

Let's work through the simplification step by step:

### Step 1: Simplify the numerator and denominator separately
- The numerator is \(\frac{x - 6}{3}\).
- The denominator is \(\frac{4x - 24}{x - 3}\).

### Step 2: Factor where possible
- The numerator \(x - 6\) cannot be factored further, but leave it as is.
- The denominator \(4x - 24\) can be factored as \(4(x - 6)\).

This gives:

\[
\frac{\frac{x - 6}{3}}{\frac{4(x - 6)}{x - 3}}
\]

### Step 3: Simplify the complex fraction
- To simplify, multiply by the reciprocal of the denominator:
  \[
  \frac{x - 6}{3} \times \frac{x - 3}{4(x - 6)}
  \]

### Step 4: Cancel common factors
- The \(x - 6\) terms cancel out, leaving:
  \[
  \frac{x - 3}{12}
  \]

### Final Answer:
The simplified form of the expression is:

\[
\frac{x - 3}{12}
\]

Do you have any questions or would you like further details? 

Here are five related questions you might consider:
1. What is a complex fraction and how is it simplified?
2. Why can we cancel out \(x - 6\) in this problem?
3. How can you factor a polynomial expression like \(4x - 24\)?
4. When is it allowed to multiply by the reciprocal in a fraction?
5. What happens if \(x = 6\) in this expression?

**Tip:** Always check for restrictions on variable values (like when a factor becomes zero). For instance, \(x = 6\) would make the original denominator zero.

Simplify the complex fraction: (x - 6) / 3 divided by (4x - 24) / (x - 3)

Learn how to simplify a complex algebraic fraction involving polynomial expressions. This problem includes key algebraic techniques like factoring and simplifying. Suitable for students in Grades 8-10.

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