Simplify by removing factors of 1.
StartFraction p squared minus 9 Over p squared minus 6 p plus 9 EndFraction
Question content area bottom
Part 1
StartFraction p squared minus 9 Over p squared minus 6 p plus 9 EndFraction

The given expression is:

\[
\frac{p^2 - 9}{p^2 - 6p + 9}
\]

### Step 1: Factor the numerator and the denominator.

- **Numerator**: \( p^2 - 9 \) is a difference of squares, so it factors as:
  \[
  p^2 - 9 = (p - 3)(p + 3)
  \]

- **Denominator**: \( p^2 - 6p + 9 \) is a perfect square trinomial, so it factors as:
  \[
  p^2 - 6p + 9 = (p - 3)(p - 3) = (p - 3)^2
  \]

### Step 2: Simplify the expression.
Now the expression becomes:
\[
\frac{(p - 3)(p + 3)}{(p - 3)^2}
\]

We can cancel out one factor of \( p - 3 \) from both the numerator and the denominator, assuming \( p \neq 3 \) to avoid division by zero.

So, the simplified expression is:
\[
\frac{p + 3}{p - 3}
\]

This is the final simplified form of the expression.

---

Do you have any questions or would you like further details? 

Here are 5 related questions:
1. How do you factor a perfect square trinomial?
2. What is the difference of squares and how is it factored?
3. Why is it necessary to assume \( p \neq 3 \) in the simplification?
4. How do you handle expressions that cannot be simplified by factoring?
5. What is the importance of simplifying rational expressions?

**Tip**: Always check for common factors between the numerator and the denominator before canceling to ensure accuracy.

Simplify by removing factors of 1. StartFraction p squared minus 9 Over p squared minus 6 p plus 9 EndFraction

Learn how to simplify the rational expression (p^2 - 9) / (p^2 - 6p + 9) by factoring the numerator and denominator. This example uses key algebraic techniques, such as factoring a difference of squares and a perfect square trinomial. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation