Simplify the following expression completely. \( \frac{5 x+30}{x^{2}-1 x-42} \) 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:

To simplify the expression \( \frac{5x + 30}{x^{2} - x - 42} \), we can start by factoring both the numerator and the denominator. The numerator \( 5x + 30 \) can be factored as: \( 5(x + 6) \). The denominator \( x^{2} - x - 42 \) can be factored by looking for two numbers that multiply to \(-42\) and add to \(-1\). These numbers are \(6\) and \(-7\), so we can write: \( (x - 7)(x + 6) \). Now, we can rewrite the expression as: \( \frac{5(x + 6)}{(x - 7)(x + 6)} \). Since \( (x + 6) \) is common in both the numerator and the denominator, we can cancel it out (as long as \( x \neq -6 \) to avoid division by zero). The resulting simplified expression is: \( \frac{5}{x - 7} \). So, the answers to the boxes are: Numerator: 5 Denominator: x - 7