Step 1 :The function given is \(f(x)=\frac{-3}{x-7}\).
Step 2 :To find where the function is increasing or decreasing, we need to find its derivative and analyze its sign.
Step 3 :The derivative of a function gives us the rate of change of the function. If the derivative is positive, the function is increasing. If the derivative is negative, the function is decreasing.
Step 4 :The derivative of the function is \(f'(x)=\frac{3}{{(x-7)}^2}\), which is always positive for all \(x \neq 7\).
Step 5 :Therefore, the function is increasing on the intervals \((-\infty, 7)\) and \((7, \infty)\).
Step 6 :The function is never decreasing.
Step 7 :\(\boxed{\text{Final Answer: The function is increasing on } (-\infty, 7) \text{ and } (7, \infty). \text{ The function is never decreasing.}}\)