Given that \( g(x)=\frac{x-6}{x+5} \), find cach of the following. \( \begin{array}{llll}\text { a) } g(9) & \text { b) } g(6) & \text { c) } g(-5) & \text { d) } g(-13.25) \\ \text { a) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. } \\ \text { a }(x+h)\end{array} \) A. \( g(9)=\frac{3}{14} \) (Simplify your answer.) B. \( g(9) \) does not exist. C. \( g(9) \) is not a real number. Belect the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( g(6)=\square \) B. \( g(6) \) does not exist C. \( g(6) \) is not a real number.

To evaluate \( g(x) = \frac{x - 6}{x + 5} \) for the provided values: **For part a) \( g(9) \):** \[ g(9) = \frac{9 - 6}{9 + 5} = \frac{3}{14} \] So the correct choice is A. \( g(9) = \frac{3}{14} \). **For part b) \( g(6) \):** \[ g(6) = \frac{6 - 6}{6 + 5} = \frac{0}{11} = 0 \] So the correct choice is A. \( g(6) = 0 \). Now let’s address the remaining parts: **For part c) \( g(-5) \):** \[ g(-5) = \frac{-5 - 6}{-5 + 5} = \frac{-11}{0} \] Since division by zero is undefined, the correct choice is B. \( g(-5) \) does not exist. **For part d) \( g(-13.25) \):** \[ g(-13.25) = \frac{-13.25 - 6}{-13.25 + 5} = \frac{-19.25}{-8.25} \approx 2.3333 \] Thus, \( g(-13.25) \) is approximately \( 2.3333 \). In summary: - a) \( g(9) = \frac{3}{14} \). (Choice A) - b) \( g(6) = 0 \). (Choice A) - c) \( g(-5) \) does not exist. (Choice B) - d) \( g(-13.25) \approx 2.3333 \).