1. **State the problem:** Simplify the expression $$\frac{ab + 3b - 2a - 6}{(a + 3)b}$$. 2. **Identify the numerator and denominator:** - Numerator: $$ab + 3b - 2a - 6$$ - Denominator: $$(a + 3)b$$ 3. **Factor the numerator:** Group terms to factor by grouping: $$ab + 3b - 2a - 6 = b(a + 3) - 2(a + 3)$$ 4. **Factor out the common binomial:** $$b(a + 3) - 2(a + 3) = (a + 3)(b - 2)$$ 5. **Rewrite the original expression using the factored form:** $$\frac{(a + 3)(b - 2)}{(a + 3)b}$$ 6. **Cancel the common factor $a + 3$ (assuming $a \neq -3$ to avoid division by zero):** $$\frac{b - 2}{b}$$ 7. **Final simplified expression:** $$\frac{b - 2}{b}$$ This is the simplified form of the original expression, valid for $a \neq -3$ and $b \neq 0$ (to avoid division by zero).