It looks like you're asking for the Average Rate of Change (ARC) of a function $g(x)$ over the interval $(-3, 1)$, with the function definition $g(x) = \frac{x - 15}{2x}$.

The formula for the Average Rate of Change (ARC) of a function $g(x)$ over an interval $[a, b]$ is:

$\text{ARC} = \frac{g(b) - g(a)}{b - a}$

Here, we are given $a = -3$ and $b = 1$.

Let's calculate it step by step:

1. Evaluate $g(1)$:

$g(1) = \frac{1 - 15}{2(1)} = \frac{-14}{2} = -7$

2. Evaluate $g(-3)$:

$g(-3) = \frac{-3 - 15}{2(-3)} = \frac{-18}{-6} = 3$

3. Find the ARC:

$\text{ARC} = \frac{g(1) - g(-3)}{1 - (-3)} = \frac{-7 - 3}{1 + 3} = \frac{-10}{4} = -\frac{5}{2}$

So, the Average Rate of Change of $g(x)$ over the interval $(-3, 1)$ is $-\frac{5}{2}$.

Would you like more details or have any questions?

Here are 5 related questions you might want to explore:

1. How do you interpret the average rate of change geometrically?
2. How is the ARC of a function related to its derivative?
3. What is the ARC for a quadratic function over a given interval?
4. How would the ARC change if the interval were different?
5. How do you calculate the instantaneous rate of change at a point?

Tip: The Average Rate of Change over an interval is similar to finding the slope of the secant line between two points on a curve!