Given that $$ g(x)=\frac{x-6}{x+5} $$, lind each of the following. a) $$ g(9) $$ b) $$ g(6) $$ c) $$ 9(-5) $$ d) $$ 9(-1325) $$ e) $$ 9(x+h) $$ C. $$ g(6) $$ is not a real number. c) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $$ g(-5)= $$ $$ \square $$ (Simplify your answer.) B. $$ g(-5) $$ does not exist. C. $$ g(-5) $$ is not a real number. d) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $$ g(-13.25)=\frac{7}{3} $$ (Type an integer or decimal rounded to three decimal places as needed.) B. $$ g(-13.25) $$ does nol exist. C. $$ g(-13.25) $$ is not a real number. e) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $$ g(x+h)=\square $$ (Simplify your answer.) $$ \square $$ B. $$ g(x+h) $$ does not exist. C. $$ g(x+h) $$ is not a real number.

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Let's solve the problem step by step.

### Given Function
The function is defined as:
$$
g(x) = \frac{x - 6}{x + 5}
$$

### Part a: Calculate $$ g(9) $$
To find $$ g(9) $$:
$$
g(9) = \frac{9 - 6}{9 + 5} = \frac{3}{14}
$$

### Part b: Calculate $$ g(6) $$
To find $$ g(6) $$:
$$
g(6) = \frac{6 - 6}{6 + 5} = \frac{0}{11} = 0
$$

### Part c: Calculate $$ 9(-5) $$
Calculating $$ 9(-5) $$:
$$
9(-5) = -45
$$

### Part d: Calculate $$ 9(-1325) $$
Calculating $$ 9(-1325) $$:
$$
9(-1325) = -11925
$$

### Part e: Calculate $$ 9(x + h) $$
Calculating $$ 9(x + h) $$:
$$
9(x + h) = 9x + 9h
$$

### Part f: Determine $$ g(-5) $$
To find $$ g(-5) $$:
$$
g(-5) = \frac{-5 - 6}{-5 + 5} = \frac{-11}{0}
$$
Since division by zero is undefined, $$ g(-5) $$ does not exist.

### Part g: Determine $$ g(-13.25) $$
To find $$ g(-13.25) $$:
$$
g(-13.25) = \frac{-13.25 - 6}{-13.25 + 5} = \frac{-19.25}{-8.25}
$$
Calculating this gives:
$$
g(-13.25) = \frac{19.25}{8.25} \approx 2.333 \text{ (rounded to three decimal places)}
$$

### Part h: Determine $$ g(x + h) $$
To find $$ g(x + h) $$:
$$
g(x + h) = \frac{(x + h) - 6}{(x + h) + 5} = \frac{x + h - 6}{x + h + 5} = \frac{x + h - 6}{x + h + 5}
$$

### Summary of Answers
- a) $$ g(9) = \frac{3}{14} $$
- b) $$ g(6) = 0 $$
- c) $$ 9(-5) = -45 $$
- d) $$ 9(-1325) = -11925 $$
- e) $$ 9(x + h) = 9x + 9h $$
- f) $$ g(-5) $$ does not exist.
- g) $$ g(-13.25) \approx 2.333 $$
- h) $$ g(x + h) = \frac{x + h - 6}{x + h + 5} $$
a) $$ g(9) = \frac{3}{14} $$ b) $$ g(6) = 0 $$ c) $$ 9(-5) = -45 $$ d) $$ 9(-1325) = -11925 $$ e) $$ 9(x + h) = 9x + 9h $$ f) $$ g(-5) $$ does not exist. g) $$ g(-13.25) \approx 2.333 $$ h) $$ g(x + h) = \frac{x + h - 6}{x + h + 5} $$

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