1. **State the problem:** Simplify the expression $$\frac{-3 - \sqrt{80}}{6}$$. 2. **Recall the rules:** To simplify, first simplify the square root if possible, then simplify the fraction by factoring and canceling common factors. 3. **Simplify the square root:** $$\sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \times \sqrt{5} = 4\sqrt{5}$$. 4. **Rewrite the expression:** $$\frac{-3 - 4\sqrt{5}}{6}$$. 5. **Check for common factors:** The numerator terms are $-3$ and $-4\sqrt{5}$, and the denominator is 6. 6. **Factor numerator if possible:** There is no common factor between 3 and 4\sqrt{5} other than 1, so we keep it as is. 7. **Simplify the fraction by dividing numerator and denominator by their greatest common divisor if any:** Since 3 and 6 share a factor 3, rewrite numerator as $-3 - 4\sqrt{5}$ and denominator as 6. We can write: $$\frac{-3 - 4\sqrt{5}}{6} = \frac{\cancel{3}(-1) - 4\sqrt{5}}{\cancel{6}}$$ But 4\sqrt{5} is not divisible by 3, so no common factor for entire numerator. 8. **Final simplified form:** $$\frac{-3 - 4\sqrt{5}}{6}$$. **Answer:** The simplified expression is $$\frac{-3 - 4\sqrt{5}}{6}$$.