The expression in the image is:

$\frac{x^2 - 2}{4x + 4}$

To simplify this rational expression, follow these steps:

Step 1: Factor the denominator

The denominator $4x + 4$ can be factored as: $4x + 4 = 4(x + 1)$

Step 2: Check the numerator for factoring

The numerator $x^2 - 2$ does not factor any further using simple algebraic methods. It is already in its simplest form as a difference of squares would require a perfect square constant, but $2$ is not a perfect square.

Step 3: Write the simplified expression

Since there are no common factors between the numerator and the denominator, the expression cannot be simplified further.

Thus, the simplified form of the expression remains:

$\frac{x^2 - 2}{4(x + 1)}$

Do you need more details or have any further questions?

Here are 5 related questions you might find useful:

1. How do you factor quadratic expressions?
2. What happens when there are common factors between the numerator and denominator in rational expressions?
3. Can we use partial fraction decomposition on this expression?
4. How does the difference of squares factorization work?
5. How do you find vertical asymptotes for rational expressions?

Tip: Always factor both the numerator and denominator of a rational expression before checking for simplification opportunities.