1. The problem is to find the least common denominator (LCD) of the given expressions. 2. The LCD is the smallest expression that contains all factors of the denominators involved. 3. Let's analyze the options: - Option A: $n(9 + n)(9 - n)$ can be rewritten using the difference of squares as $n(81 - n^2)$. - Option B: $n + 9$ is a linear binomial. - Option C: $n^2 + 81$ is a sum of squares, which does not factor over the reals. - Option D: $81n^2$ is a product of constants and $n^2$. 4. Since the denominators likely involve factors of $n$, $9+n$, and $9-n$, the LCD must include all these factors. 5. Option A explicitly includes $n$, $9+n$, and $9-n$, making it the least common denominator. Final answer: Option A: $n(9 + n)(9 - n)$