1. **State the problem:** Reduce the expression $$\frac{3a^2 + 3ab}{3a^2 + 6ab + 3b^2}$$ to its lowest terms. 2. **Identify the formula and rules:** To simplify a rational expression, factor both numerator and denominator and then cancel common factors. 3. **Factor the numerator:** $$3a^2 + 3ab = 3a(a + b)$$ 4. **Factor the denominator:** $$3a^2 + 6ab + 3b^2 = 3(a^2 + 2ab + b^2) = 3(a + b)^2$$ 5. **Rewrite the expression:** $$\frac{3a(a + b)}{3(a + b)^2}$$ 6. **Cancel common factors:** Cancel 3 and one factor of $(a + b)$: $$\frac{a}{a + b}$$ 7. **Final answer:** The expression reduced to its lowest form is $$\frac{a}{a + b}$$.