To simplify the expression:

\[
\frac{x^2 - 4x + 4}{3x - 6}
\]

### Step 1: Factor the numerator and denominator (if possible).

1. **Numerator** \(x^2 - 4x + 4\):  
   This is a perfect square trinomial and can be factored as:
   \[
   x^2 - 4x + 4 = (x - 2)^2
   \]

2. **Denominator** \(3x - 6\):  
   Factor out the greatest common factor (GCF), which is 3:
   \[
   3x - 6 = 3(x - 2)
   \]

### Step 2: Simplify the expression.

Now, rewrite the expression using these factored forms:
\[
\frac{(x - 2)^2}{3(x - 2)}
\]

Since \(x - 2\) appears in both the numerator and denominator, you can cancel one factor of \(x - 2\) (as long as \(x \neq 2\), to avoid division by zero):

\[
\frac{x - 2}{3}
\]

### Final simplified form:
\[
\frac{x - 2}{3} \quad \text{(for } x \neq 2\text{)}
\]

Would you like more details on this simplification or have any questions?

Here are 5 related questions you might consider:

1. How do you identify perfect square trinomials in general?
2. What is the general process for factoring trinomials?
3. Why is it important to check for restrictions (like \(x \neq 2\)) after canceling terms?
4. How do you factor expressions that aren't perfect squares?
5. What is the process for simplifying rational expressions involving higher powers?

**Tip:** Always check for restrictions (e.g., values that make the denominator zero) when simplifying algebraic expressions.

Simplify the rational expression x² - 4x + 4 / 3x - 6 by factoring and reducing common terms. This solution covers factoring techniques and simplifying rational expressions, ideal 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