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.