1. **Problem:** Simplify the rational expression $$\frac{3(x + 2)}{9(x + 3)}$$ given $$x \neq -3$$. 2. **Formula and rules:** To simplify a rational expression, factor numerator and denominator and cancel common factors. 3. **Step 1:** Factor numerator and denominator: $$\frac{3(x + 2)}{9(x + 3)} = \frac{3(x + 2)}{3 \cdot 3 (x + 3)}$$ 4. **Step 2:** Cancel common factor 3: $$\frac{\cancel{3}(x + 2)}{\cancel{3} \cdot 3 (x + 3)} = \frac{x + 2}{3(x + 3)}$$ 5. **Answer:** The simplified form is $$\frac{x + 2}{3(x + 3)}$$ with restriction $$x \neq -3$$. This is the first problem in your message. Other problems are not solved as per instructions.