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The problem asks to find the remainder (residuo) of the operation:

\[
\frac{3x^2 - 3x}{x - 1}
\]

To solve this, we perform polynomial division. Here's the process:

### Step 1: Divide the first term of the numerator by the first term of the denominator.
The first term of the numerator is \(3x^2\), and the first term of the denominator is \(x\). 

\[
\frac{3x^2}{x} = 3x
\]

So, the first part of the quotient is \(3x\).

### Step 2: Multiply \(3x\) by the entire denominator \((x - 1)\).
\[
3x \cdot (x - 1) = 3x^2 - 3x
\]

### Step 3: Subtract the result from the original polynomial.
Now subtract \(3x^2 - 3x\) from \(3x^2 - 3x\):

\[
(3x^2 - 3x) - (3x^2 - 3x) = 0
\]

### Conclusion:
Since the subtraction results in zero, the remainder (residuo) of the operation is **0**.

Let me know if you'd like more details, or if you have any questions!

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Here are five related questions to consider:
1. How do we apply polynomial division to higher-degree polynomials?
2. What happens if the remainder is non-zero in polynomial division?
3. Can synthetic division be used for this type of problem?
4. How does the remainder theorem relate to polynomial division?
5. What are some applications of polynomial division in real-world problems?

**Tip**: Always check if the polynomial can be factored before dividing—it might simplify the process.

¿Cuál es el residuo de la operación (3x^2 - 3x) ÷ (x - 1)?

Discover how to find the remainder of the polynomial division (3x^2 - 3x) ÷ (x - 1). This solution involves polynomial division and the remainder theorem. Ideal for high school students learning about polynomial functions and algebraic division.

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