https://file.aiquickdraw.com/mathbot/file/1726148366002efgc3c1c.jpg

The expression given in the image is:

\[
\frac{n^2}{9a + n} - \frac{81a^2}{9a + n}
\]

### Steps to Simplify:

1. **Common Denominator:**
   Since the denominators are already the same (\(9a + n\)), we can directly subtract the numerators:
   \[
   \frac{n^2}{9a + n} - \frac{81a^2}{9a + n} = \frac{n^2 - 81a^2}{9a + n}
   \]

2. **Difference of Squares:**
   Notice that the numerator \(n^2 - 81a^2\) is a difference of squares:
   \[
   n^2 - 81a^2 = (n - 9a)(n + 9a)
   \]

   So, the expression becomes:
   \[
   \frac{(n - 9a)(n + 9a)}{9a + n}
   \]

3. **Simplification:**
   Now, observe that \(n + 9a = 9a + n\), so we can cancel out this common factor from the numerator and the denominator:
   \[
   \frac{(n - 9a)(n + 9a)}{9a + n} = n - 9a
   \]

Thus, the simplified expression is:
\[
n - 9a
\]

### Answer:
The answer to the problem is \(n - 9a\), so the boxes should be filled in as:

\[
\boxed{n} - \boxed{9} \boxed{a}
\]

---

Would you like further details on any step? Here are a few related questions to consider:

1. How does the difference of squares formula work in general?
2. What are the conditions for canceling terms in fractions?
3. How can you handle subtraction of rational expressions with different denominators?
4. What if the terms in the denominator weren't identical—how would the process change?
5. How can we factor other types of polynomials, like cubics?

**Tip:** Always check for special factorizations (like the difference of squares) when simplifying algebraic expressions.

Simplify the expression: (n^2) / (9a + n) - (81a^2) / (9a + n)

Learn how to simplify the rational expression n^2/(9a + n) - 81a^2/(9a + n) by factoring the difference of squares and canceling common terms. This example is suitable for students in Grades 8-10.

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