\( f(x)=3 x-1 \) \( g(x)=x^{2}-x \) Find \( \left(\frac{f}{g}\right)(x) \)

To find \(\left(\frac{f}{g}\right)(x)\), we need to compute the ratio of the two functions \(f(x)\) and \(g(x)\). 1. We start by substituting the functions into the ratio: \[ \left(\frac{f}{g}\right)(x) = \frac{f(x)}{g(x)} = \frac{3x - 1}{x^2 - x} \] 2. The next step is to ensure the denominator is not zero. The function \(g(x) = x^2 - x\) can be factored: \[ g(x) = x(x - 1) \] So, \(g(x) = 0\) when \(x = 0\) or \(x = 1\). Thus, the final result is: \[ \left(\frac{f}{g}\right)(x) = \frac{3x - 1}{x(x - 1)}, \quad \text{for } x \neq 0 \text{ and } x \neq 1. \]