1. **State the problem:** Divide the two rational expressions $\frac{x+5}{6}$ and $\frac{4x+20}{5}$. Simplify the result. 2. **Recall the division rule for fractions:** Dividing by a fraction is the same as multiplying by its reciprocal. So, $$\frac{x+5}{6} \div \frac{4x+20}{5} = \frac{x+5}{6} \times \frac{5}{4x+20}$$ 3. **Factor where possible:** Notice that $4x+20$ can be factored as $4(x+5)$. 4. **Rewrite the expression:** $$\frac{x+5}{6} \times \frac{5}{4(x+5)}$$ 5. **Simplify common factors:** The $(x+5)$ terms cancel out (assuming $x \neq -5$ to avoid division by zero). 6. **Multiply the remaining terms:** $$\frac{1}{6} \times \frac{5}{4} = \frac{5}{24}$$ 7. **State the domain restriction:** Since we canceled $(x+5)$, $x \neq -5$. **Final answer:** $$\frac{x+5}{6} \div \frac{4x+20}{5} = \frac{5}{24}, \quad x \neq -5$$