1. **State the problem:** Multiply the expressions $$\frac{x}{x+3} \cdot \frac{x+3}{4}$$. 2. **Recall the multiplication rule for fractions:** When multiplying fractions, multiply the numerators together and the denominators together: $$\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}$$ 3. **Apply the rule:** $$\frac{x}{x+3} \cdot \frac{x+3}{4} = \frac{x \cdot (x+3)}{(x+3) \cdot 4}$$ 4. **Simplify by canceling common factors:** The term $$x+3$$ appears in both numerator and denominator, so it cancels out (assuming $$x \neq -3$$ to avoid division by zero): $$\frac{x \cdot \cancel{(x+3)}}{\cancel{(x+3)} \cdot 4} = \frac{x}{4}$$ 5. **Final answer:** $$\boxed{\frac{x}{4}}$$ This corresponds to option A.