Simplify the following expression completely. \( \frac{x^{2}-2 x-8}{x^{2}+7 x+10} \) Enter the numerator and denominator separately in the boxes below. If the denominator is 1 , enter the number 1. Do not leave either box blank. Answer: Numerator preview: Denominator preview: Question Help:

To simplify the expression \( \frac{x^{2}-2 x-8}{x^{2}+7 x+10} \), we need to factor both the numerator and the denominator. First, let's factor the numerator: The expression \( x^{2} - 2x - 8 \) can be factored as \( (x - 4)(x + 2) \). Next, we factor the denominator: The expression \( x^{2} + 7x + 10 \) can be factored as \( (x + 5)(x + 2) \). Now, substituting our factored forms back into the expression, we have: \( \frac{(x - 4)(x + 2)}{(x + 5)(x + 2)} \). We can see that \( (x + 2) \) is a common factor in both the numerator and the denominator, allowing us to cancel it out (as long as \( x \neq -2 \)): Thus, the simplified expression is: \( \frac{x - 4}{x + 5} \). Now, to fill in the answer boxes: Numerator preview: \( x - 4 \) Denominator preview: \( x + 5 \)