It seems like you have the expression:

$\frac{x^2 - 5x - 14}{x^2 + 4x + 4}$

Would you like to simplify this expression, factor it, or solve for specific values of $x$? Let me know what you're looking for!

If you’d like to factor both the numerator and the denominator:

Factoring the denominator:

The denominator is $x^2 + 4x + 4$, which is a perfect square trinomial:

$x^2 + 4x + 4 = (x + 2)^2$

Factoring the numerator:

For the numerator, $x^2 - 5x - 14$, we look for two numbers that multiply to $-14$ and add up to $-5$. These numbers are $-7$ and $2$, so we can factor it as:

$x^2 - 5x - 14 = (x - 7)(x + 2)$

Now, the expression becomes:

$\frac{(x - 7)(x + 2)}{(x + 2)^2}$

Simplification:

You can cancel the common factor of $(x + 2)$ in the numerator and denominator (as long as $x \neq -2$, since division by zero is undefined):

$\frac{x - 7}{x + 2}$

So, the simplified expression is:

$\frac{x - 7}{x + 2}$

Would you like more details on this process, or do you need help with another step?

Related questions:

1. What happens when $x = -2$ in the original expression?
2. How can you use the factored form to solve for specific values of $x$?
3. What is the domain of the expression $\frac{x^2 - 5x - 14}{x^2 + 4x + 4}$?
4. How do you identify a perfect square trinomial?
5. How would you solve an equation using this simplified form?

Tip: When simplifying rational expressions, always look for common factors between the numerator and denominator to cancel them out.