The expression in the image appears to be:

$\frac{x + 4}{3x} \div \frac{2x + 8}{1}.$

Simplification Process:

1. Rewrite the division of fractions as multiplication: $\frac{x + 4}{3x} \times \frac{1}{2x + 8}.$

2. Factorize any terms where possible:

   • $x + 4$ remains as is.
   • $2x + 8 = 2(x + 4).$

   Substituting, the expression becomes: $\frac{x + 4}{3x} \times \frac{1}{2(x + 4)}.$

3. Cancel out the common factor $x + 4$ in the numerator and denominator: $\frac{1}{3x} \times \frac{1}{2}.$

4. Multiply the simplified fractions: $\frac{1}{3x \cdot 2} = \frac{1}{6x}.$

Final Answer:

$\boxed{\frac{1}{6x}}$

Let me know if you have questions or want additional clarifications.

Here are 5 related questions to explore:

1. How do you simplify fractions involving division of polynomials?
2. What is the importance of factoring in simplifying algebraic expressions?
3. How would the result change if the numerator and denominator had different terms?
4. Can this expression be evaluated for specific values of $x$? What are the restrictions?
5. How does this process differ if additional variables are included?

Tip: Always check for common factors that can be canceled to simplify the expression effectively.