The given expression for \( y \) is:

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

To simplify this expression, let's follow these steps:

1. Factor the denominator.

\[ x^2 + 4x + 4 \]

This is a quadratic expression, which can be factored as:

\[ (x + 2)(x + 2) \]
\[ x^2 + 4x + 4 = (x + 2)^2 \]

2. Substitute the factored form back into the expression.

\[ y = \frac{4x}{(x + 2)^2} \]

So the simplified expression for \( y \) is:

\[ y = \frac{4x}{(x + 2)^2} \]

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

Here are some related questions that you might find useful:
1. How do you factor quadratic expressions in general?
2. Can you provide another example of simplifying a rational expression?
3. What are the key properties of rational functions?
4. How do you determine the domain of a rational function?
5. How do you find vertical asymptotes of a rational function?
6. What is the process for simplifying complex rational expressions?
7. How does factoring help in simplifying expressions and solving equations?
8. Can you explain how to graph a rational function like \( y = \frac{4x}{(x + 2)^2} \)?

**Tip:** When simplifying rational expressions, always look for common factors in the numerator and the denominator to factor out and reduce the expression.

Learn how to simplify the rational expression 4x / (x^2 + 4x + 4) step-by-step. This problem involves factorization of quadratic equations and simplification of rational expressions. Suitable for students in Grades 9-12.

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