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

To find \( g(9) \), we substitute \( x \) with \( 9 \) in the function: \[ g(9) = \frac{9 - 6}{9 + 5} = \frac{3}{14} \] So, we have: A. \( g(9) = \frac{3}{14} \). Now, let’s find \( g(6) \): \[ g(6) = \frac{6 - 6}{6 + 5} = \frac{0}{11} = 0 \] Next, \( g(-5) \): \[ g(-5) = \frac{-5 - 6}{-5 + 5} = \frac{-11}{0} \] Since division by zero is undefined, we have: B. \( g(-5) \) does not exist. Finally, for \( g(-13.25) \): \[ g(-13.25) = \frac{-13.25 - 6}{-13.25 + 5} = \frac{-19.25}{-8.25} = \frac{19.25}{8.25} = \frac{19.25 \div 8.25}{8.25 \div 8.25} = \frac{19.25 \div 8.25}{1} = \frac{19.25}{8.25} \] Thus, we conclude: A. \( g(9) = \frac{3}{14} \); B. \( g(-5) \) does not exist.