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The given problem is asking to find \( \left(\frac{f}{g}\right)(x) \), where:

- \( f(x) = 3x - 1 \)
- \( g(x) = x^2 - x \)

To find \( \left(\frac{f}{g}\right)(x) \), we need to divide \( f(x) \) by \( g(x) \):

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

This is the expression for \( \left(\frac{f}{g}\right)(x) \). There are no further simplifications possible unless the denominator or numerator can be factored in such a way that common terms can be canceled. However, here the terms are already in their simplest form.

### Final Answer:
\[
\left(\frac{f}{g}\right)(x) = \frac{3x - 1}{x^2 - x}
\]

Would you like further details on simplifying or analyzing this expression?

Here are five related questions:
1. How would you compute the domain of \( \left(\frac{f}{g}\right)(x) \)?
2. How can you factor the denominator \( x^2 - x \)?
3. What happens to \( \left(\frac{f}{g}\right)(x) \) at values where \( g(x) = 0 \)?
4. How would you find the x-intercepts of \( \frac{f(x)}{g(x)} \)?
5. What is the asymptotic behavior of \( \frac{f(x)}{g(x)} \) as \( x \to \infty \)?

**Tip:** Always check for points where the denominator becomes zero to avoid division by zero when working with rational functions.

Given functions f(x) = 3x - 1 and g(x) = x^2 - x, find (f/g)(x).

Learn how to find (f/g)(x) given f(x) = 3x - 1 and g(x) = x^2 - x. This problem explores rational functions and division of functions, suitable for students in Grades 9-11.

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