We are given the function $f(x) = \frac{3x^2 - x}{x - 1}$ and asked to find the equation of its oblique asymptote.

1. Problem Description

We are given the function $f(x) = \frac{3x^2 - x}{x - 1}$ and asked to find the equation of its oblique asymptote.

2. Solution Steps

To find the oblique asymptote, we perform polynomial long division of the numerator by the denominator.

Dividing $3x^2 - x$ by $x - 1$, we have:

```

3x + 2

x - 1 | 3x^2 - x

-(3x^2 - 3x)

----------------

2x

-(2x - 2)

----------------

2

```

So, $\frac{3x^2 - x}{x - 1} = 3x + 2 + \frac{2}{x - 1}$.

As $x$ approaches infinity, the term $\frac{2}{x - 1}$ approaches

0. Therefore, the oblique asymptote is $y = 3x + 2$.

3. Final Answer

$y = 3x + 2$