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The problem asks to perform multiplication or division and then simplify the expressions given. Let's start with the first expression:

### First Expression
\[ \frac{4x}{x^2 - 4} \cdot \frac{x + 2}{16x} \]

1. **Factorize** each polynomial where possible:
   - \( x^2 - 4 \) can be factored as a difference of squares: \( (x-2)(x+2) \).
   - \( 16x \) remains as is.

2. **Rewrite** the expression with the factors:
   \[ \frac{4x}{(x-2)(x+2)} \cdot \frac{x+2}{16x} \]

3. **Simplify** by cancelling out common terms:
   - The \( x+2 \) terms cancel out.
   - \( x \) in the numerator and denominator can be partially cancelled, and \( 4 \) can be simplified with \( 16 \) to give \( \frac{1}{4} \).

4. The simplified expression is:
   \[ \frac{1}{4(x-2)} \]

Now, I'll continue with the next expressions. If you have any specific request among these or need further simplifications or explanations for this one, feel free to ask!

Would you like to proceed with a specific expression or need details on the steps? Here are some additional questions you might consider:
1. How do you factorize a polynomial?
2. Why is it important to cancel out terms before multiplying?
3. Can you provide an example of division involving polynomials?
4. How do you handle expressions where variables cancel each other out completely?
5. What is the significance of finding the least common denominator in complex rational expressions?

**Tip:** Always check for common factors in the numerator and denominator to simplify expressions efficiently.

Efectúe la multiplicación o división, y simplifique las siguientes expresiones algebraicas.

Aprende a realizar la multiplicación o división de expresiones algebraicas y a simplificarlas utilizando factorización y reglas de fracciones. Este ejercicio cubre conceptos importantes de álgebra, incluyendo la factorización de polinomios y la simplificación de fracciones algebraicas.

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