Simplify the following expression completely. \( \frac{x^{2}-8 x+12}{x^{2}+5 x-14} \) 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 \( \frac{x^{2}-8 x+12}{x^{2}+5 x-14} \), we first factor both the numerator and the denominator. For the numerator \( x^{2}-8x+12 \): We are looking for two numbers that multiply to \( 12 \) and add up to \( -8 \). These numbers are \( -6 \) and \( -2 \). Thus, we can factor it as: \( x^{2}-8x+12 = (x-6)(x-2) \). For the denominator \( x^{2}+5x-14 \): We are looking for two numbers that multiply to \( -14 \) and add up to \( 5 \). These numbers are \( 7 \) and \( -2 \). Thus, we can factor it as: \( x^{2}+5x-14 = (x+7)(x-2) \). Now we can rewrite the expression as: \[ \frac{(x-6)(x-2)}{(x+7)(x-2)} \] Notice that \( (x-2) \) can be canceled from both the numerator and denominator, leading to: \[ \frac{x-6}{x+7} \] Thus, the simplified expression has: Numerator: \( x-6 \) Denominator: \( x+7 \)