https://file.aiquickdraw.com/mathbot/file/1726404336947c5k97d6z.jpg

The problem in the image is:

\[
\frac{9x^2 - 1}{9x + 3}
\]

Let's simplify it step-by-step.

### Step 1: Factor the numerator
The numerator, \( 9x^2 - 1 \), is a difference of squares, so it can be factored as:
\[
9x^2 - 1 = (3x - 1)(3x + 1)
\]

### Step 2: Rewrite the expression
Now, the expression becomes:
\[
\frac{(3x - 1)(3x + 1)}{9x + 3}
\]

### Step 3: Factor the denominator
Factor out the common factor from the denominator:
\[
9x + 3 = 3(3x + 1)
\]

### Step 4: Cancel common terms
Now the expression is:
\[
\frac{(3x - 1)(3x + 1)}{3(3x + 1)}
\]
Since \( 3x + 1 \) is a common factor in both the numerator and denominator, we can cancel it out:
\[
\frac{3x - 1}{3}
\]

### Final simplified expression:
\[
\frac{3x - 1}{3}
\]

Would you like more details on any step or have any questions?

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Here are 5 related questions to expand your understanding:

1. How do you factor a difference of squares?
2. What other types of factoring techniques can be applied to quadratic expressions?
3. How do you handle cases where the denominator cannot be factored?
4. Why is it important to simplify expressions by canceling common terms?
5. Can you solve similar problems involving rational expressions with higher powers?

**Tip**: Always check for common factors in both the numerator and denominator before canceling terms in rational expressions.

Learn how to simplify the rational expression (9x^2 - 1) / (9x + 3) by factoring using the difference of squares and canceling common terms. This detailed solution is suitable for students in Grades 9-10.

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