1. **State the problem:** Simplify the expression $$\frac{-3 + (-2 - 9) - 1}{(-5)(-2 - 3 + 6)}$$. 2. **Simplify the numerator:** Calculate inside the parentheses first: $$-2 - 9 = -11$$ So numerator becomes: $$-3 + (-11) - 1$$ Simplify step-by-step: $$-3 + (-11) = -14$$ $$-14 - 1 = -15$$ 3. **Simplify the denominator:** Calculate inside the parentheses: $$-2 - 3 + 6 = (-2 - 3) + 6 = -5 + 6 = 1$$ So denominator becomes: $$(-5)(1) = -5$$ 4. **Rewrite the fraction:** $$\frac{-15}{-5}$$ 5. **Simplify the fraction:** Divide numerator and denominator by their common factor 5: $$\frac{\cancel{-15}^{3} \times 5}{\cancel{-5}^{1} \times 5} = \frac{3}{1}$$ Since both numerator and denominator are negative, the fraction is positive: $$\frac{-15}{-5} = 3$$ **Final answer:** $$3$$