https://file.aiquickdraw.com/mathbot/file/1726668347151lrv5v2o0.jpg

The expression in the image is:

\[
\frac{2a^2 - 8}{2a - 4}
\]

You are likely being asked to simplify this expression.

### Step-by-step simplification:

1. **Factor the numerator** \( 2a^2 - 8 \):
   \[
   2a^2 - 8 = 2(a^2 - 4) = 2(a - 2)(a + 2)
   \]
   This is a difference of squares.

2. **Factor the denominator** \( 2a - 4 \):
   \[
   2a - 4 = 2(a - 2)
   \]

3. Now rewrite the expression:
   \[
   \frac{2(a - 2)(a + 2)}{2(a - 2)}
   \]

4. Cancel out the common terms \( 2(a - 2) \) from both numerator and denominator:
   \[
   a + 2
   \]

Thus, the simplified expression is:

\[
a + 2
\]

### Final Answer: \( a + 2 \)

Would you like further clarification on this, or do you have any questions?

Here are five related questions for practice:
1. What is the general rule for factoring differences of squares?
2. How would you simplify \(\frac{x^2 - 9}{x - 3}\)?
3. What happens when a numerator or denominator cannot be factored?
4. How can you check if your simplified expression is correct?
5. What is the difference between factoring and simplifying?

**Tip**: Always look for common factors to cancel out when simplifying rational expressions!

Simplify the expression (2a^2 - 8) ÷ (2a - 4) at a = 2.

Learn how to simplify the rational expression (2a^2 - 8) ÷ (2a - 4) by factoring and canceling common terms. This problem demonstrates key algebraic concepts, such as factoring and simplifying fractions. Suitable for students in Grades 8-10.

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