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The image shows another rational algebraic expression that we need to simplify. Let's go through the steps.

### Given Expression:

\[
\frac{x^2 + x - 20}{x + 3} \cdot \frac{x + 1}{x - 4}
\]

### Simplification Steps:

1. **Factor the Numerators and Denominators**:
   - The quadratic expression \(x^2 + x - 20\) can be factored. We look for two numbers that multiply to \(-20\) and add to \(+1\).
     - These numbers are \(5\) and \(-4\), so:
     \[
     x^2 + x - 20 = (x + 5)(x - 4)
     \]
   
   Substituting the factored form, the expression becomes:
   
   \[
   \frac{(x + 5)(x - 4)}{x + 3} \cdot \frac{x + 1}{x - 4}
   \]

2. **Cancel Common Factors**:
   - The \(x - 4\) terms in the numerator and denominator cancel out.

   This leaves us with:

   \[
   \frac{x + 5}{x + 3} \cdot \frac{x + 1}{1}
   \]

3. **Multiply the Remaining Terms**:
   - Now multiply the remaining numerators and denominators:

   \[
   \frac{(x + 5)(x + 1)}{x + 3}
   \]

### Final Answer:

The simplified form of the expression is:

\[
\frac{(x + 5)(x + 1)}{x + 3}
\]

Would you like to explore this problem in more detail or have any specific questions?

Here are five related questions to consider:

1. How can we factor quadratic expressions quickly and effectively?
2. What should be checked before canceling terms in rational expressions?
3. How does multiplying rational expressions differ from adding them?
4. What would the domain of the simplified expression be?
5. How does the presence of multiple factors affect the simplification process?

**Tip:** When working with rational expressions, always be cautious of terms that might be canceled and ensure they do not equal zero, as this would make the original expression undefined.

Learn how to simplify the rational algebraic expression (x^2 + x - 20) / (x + 3) * (x + 1) / (x - 4) step-by-step with a detailed solution. This problem involves factoring quadratic expressions and cancelling common factors in rational expressions. Suitable for high school students.

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