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The given problem asks to find the expression equivalent to:

\[
\frac{m+3}{m^2 - 16} \div \frac{m^2 - 9}{m + 4}
\]

### Step-by-step solution:

1. **Rewrite the expression**:
   The expression can be rewritten as:

   \[
   \frac{m+3}{m^2 - 16} \times \frac{m + 4}{m^2 - 9}
   \]

   This happens because dividing by a fraction is the same as multiplying by its reciprocal.

2. **Factor the quadratic expressions**:
   - \( m^2 - 16 \) is a difference of squares: 
     \[
     m^2 - 16 = (m - 4)(m + 4)
     \]
   - \( m^2 - 9 \) is also a difference of squares:
     \[
     m^2 - 9 = (m - 3)(m + 3)
     \]

3. **Substitute the factored forms**:
   Now substitute the factored forms into the expression:

   \[
   \frac{m + 3}{(m - 4)(m + 4)} \times \frac{m + 4}{(m - 3)(m + 3)}
   \]

4. **Simplify the expression**:
   Cancel out the common factors:
   - \( m + 3 \) cancels with \( m + 3 \),
   - \( m + 4 \) cancels with \( m + 4 \).

   The simplified expression becomes:

   \[
   \frac{1}{(m - 4)(m - 3)}
   \]

Thus, the expression equivalent to the original one is:

\[
\boxed{\frac{1}{(m - 4)(m - 3)}}
\]

This matches option B in the given choices.

---

Would you like more details on this explanation or have any further questions?

Here are some related questions you can explore:
1. How do you factor a quadratic expression like \( m^2 - 16 \)?
2. What is the process of simplifying algebraic fractions?
3. How can you identify and factor a difference of squares?
4. What are the rules for multiplying and dividing rational expressions?
5. How does cancelling common factors work in algebraic fractions?

**Tip**: Always check for factorable expressions in both the numerator and denominator when simplifying algebraic fractions.

Which expression is equivalent to the expression below?
(m+3) / (m^2 - 16) ÷ (m^2 - 9) / (m+4)

Learn how to simplify the expression (m+3)/(m^2-16) ÷ (m^2-9)/(m+4) by factoring quadratics and applying rules for division of rational expressions. This problem explores key algebraic concepts such as the difference of squares and simplifying fractions.

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