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.