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The problem displayed in the image is to simplify a complex fraction. The given expression is:

\[
\frac{\frac{x^2 - 2x - 15}{8x - 24}}{\frac{x^2 - 25}{4x + 20}}
\]

### Step-by-step simplification:

1. **Factor each part of the complex fraction:**
   - The numerator of the first fraction is \(x^2 - 2x - 15\), which factors as:
     \[
     (x - 5)(x + 3)
     \]
   - The denominator of the first fraction is \(8x - 24\), which can be factored as:
     \[
     8(x - 3)
     \]
   - The numerator of the second fraction is \(x^2 - 25\), which is a difference of squares and factors as:
     \[
     (x - 5)(x + 5)
     \]
   - The denominator of the second fraction is \(4x + 20\), which factors as:
     \[
     4(x + 5)
     \]

2. **Rewrite the complex fraction:**
   The complex fraction now becomes:
   \[
   \frac{\frac{(x - 5)(x + 3)}{8(x - 3)}}{\frac{(x - 5)(x + 5)}{4(x + 5)}}
   \]

3. **Simplify the complex fraction:**
   When dividing fractions, you multiply by the reciprocal of the second fraction:
   \[
   \frac{(x - 5)(x + 3)}{8(x - 3)} \times \frac{4(x + 5)}{(x - 5)(x + 5)}
   \]
   Now, cancel common factors:
   - \(x - 5\) appears in both the numerator and denominator, so cancel it.
   - \(x + 5\) appears in both the numerator and denominator, so cancel it.
   
   After cancellations, you are left with:
   \[
   \frac{(x + 3) \cdot 4}{8(x - 3)}
   \]
   Simplify the constants:
   \[
   \frac{4(x + 3)}{8(x - 3)} = \frac{x + 3}{2(x - 3)}
   \]

Thus, the simplified form of the complex fraction is:

\[
\frac{x + 3}{2(x - 3)}
\]

Let me know if you need more details or have any questions!

### Related Questions:
1. How do you simplify a fraction when there are variables in both the numerator and denominator?
2. What are the steps to factor a quadratic expression like \(x^2 - 2x - 15\)?
3. What is the difference of squares, and how do you factor it?
4. How do you deal with complex fractions involving binomials?
5. What are some techniques to check if a rational expression can be further simplified?

### Tip:
When working with complex fractions, always factor first to identify and cancel common terms for faster simplification.

Simplify the complex fraction \(\frac{\frac{x^2 - 2x - 15}{8x - 24}}{\frac{x^2 - 25}{4x + 20}}\). Reduce your answer as much as possible.

Learn how to simplify a complex fraction involving rational expressions by factoring trinomials and applying the difference of squares. This detailed solution is suitable for high school students in Grades 10-12.

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