1. **Problem:** Find the least common denominator (LCD) for the expression $$\frac{3}{x+4} + \frac{x}{x^2 - 16} + \frac{x+2}{4}$$ 2. **Step 1: Factor all denominators.** - The first denominator is already factored: $x+4$ - The second denominator is a difference of squares: $$x^2 - 16 = (x-4)(x+4)$$ - The third denominator is $4$, which is $2^2$ (a constant). 3. **Step 2: Identify the LCD.** - The LCD must include each factor the greatest number of times it appears in any denominator. - From denominators: $x+4$, $(x-4)(x+4)$, and $4 = 2^2$ - So, LCD = $4(x-4)(x+4)$ 4. **Step 3: Explanation:** - We include $(x+4)$ and $(x-4)$ because they appear in the second denominator. - We include $4$ because it is the denominator of the third fraction. **Final answer:** $$\boxed{4(x-4)(x+4)}$$ --- **Summary:** The least common denominator for $$\frac{3}{x+4} + \frac{x}{x^2 - 16} + \frac{x+2}{4}$$ is $$4(x-4)(x+4)$$.