https://file.aiquickdraw.com/mathbot/file/1726147909117f7tm4ak2.jpg

The expression in the image is:

\[
\frac{8x^2y + 8xy^2}{4x^3y^2 + 4x^2y^3}
\]

Let's simplify this step by step:

1. **Factor out the greatest common factor (GCF)** from both the numerator and the denominator.

- **Numerator**: 
  \[
  8x^2y + 8xy^2 = 8xy(x + y)
  \]
  
- **Denominator**:
  \[
  4x^3y^2 + 4x^2y^3 = 4x^2y^2(x + y)
  \]

2. **Simplify the fraction** by canceling common factors:
   \[
   \frac{8xy(x + y)}{4x^2y^2(x + y)}
   \]
   Here, \(x + y\) cancels out from both the numerator and denominator, leaving:
   \[
   \frac{8xy}{4x^2y^2}
   \]

3. **Further simplify**:
   \[
   \frac{8}{4} = 2, \quad \frac{x}{x^2} = \frac{1}{x}, \quad \frac{y}{y^2} = \frac{1}{y}
   \]
   So, the simplified expression is:
   \[
   \frac{2}{xy}
   \]

Thus, the simplified form of the given expression is:

\[
\frac{2}{xy}
\]

Would you like more details on any specific step or further clarifications?

Here are 5 related questions for practice:
1. How do you find the greatest common factor of terms with variables?
2. What happens when you divide exponents with the same base?
3. How can you factor more complex polynomials?
4. How do you simplify rational expressions?
5. What are some examples of expressions that cannot be simplified?

**Tip:** When simplifying, always check for common factors across terms in both the numerator and the denominator!

Simplify the following expression: \(\frac{8x^2y + 8xy^2}{4x^3y^2 + 4x^2y^3}\)

Simplify the expression \(\frac{8x^2y + 8xy^2}{4x^3y^2 + 4x^2y^3}\) by factoring out the greatest common factor (GCF) and applying exponent rules. This problem covers key algebraic concepts, including polynomial simplification and GCF. Suitable for students in Grades 9-11.

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