https://file.aiquickdraw.com/mathbot/file/1726147111548b6xxs8cx.jpg

The expression in the image appears to be:

\[
\frac{2x^2 + 2xy}{4xy - 4y^2}
\]

Let’s simplify this step by step:

### Step 1: Factor the numerator and denominator
- The numerator is \( 2x^2 + 2xy \). We can factor out \( 2x \):
  \[
  2x(x + y)
  \]
  
- The denominator is \( 4xy - 4y^2 \). We can factor out \( 4y \):
  \[
  4y(x - y)
  \]

### Step 2: Substitute the factored forms
Now we have the expression:
\[
\frac{2x(x + y)}{4y(x - y)}
\]

### Step 3: Simplify the fraction
We can simplify the fraction by canceling out common factors. The common factor between the numerator and denominator is 2, so we divide both by 2:
\[
\frac{x(x + y)}{2y(x - y)}
\]

Thus, the simplified form of the expression is:
\[
\frac{x(x + y)}{2y(x - y)}
\]

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Would you like more details on any of these steps or additional examples?

Here are five related questions:
1. How do you factor trinomials with more complex terms?
2. How can we simplify expressions with more variables?
3. What are the rules for factoring common terms in both the numerator and denominator?
4. How does factoring help in solving algebraic equations?
5. Can we apply the same approach to rational expressions involving higher powers?

**Tip**: Always check for common factors before attempting any other simplification technique!

Simplify the algebraic expression: (2x^2 + 2xy) / (4xy - 4y^2)

This page explains how to simplify the rational expression (2x^2 + 2xy) / (4xy - 4y^2) by factoring common terms. Step-by-step guidance on algebraic factoring and simplification is provided, ideal for students in Grades 9-10.

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