1. **State the problem:** Find the limit $$\lim_{n \to \infty} \frac{n \log n}{n^2 - n}$$. 2. **Recall the formula and rules:** When evaluating limits involving infinity, compare the growth rates of numerator and denominator. Here, $n^2$ grows faster than $n \log n$. 3. **Simplify the expression:** $$\frac{n \log n}{n^2 - n} = \frac{n \log n}{n(n - 1)} = \frac{\log n}{n - 1}$$ 4. **Evaluate the limit:** As $n \to \infty$, $\log n$ grows slowly, but $n - 1$ grows without bound. 5. **Apply limit:** $$\lim_{n \to \infty} \frac{\log n}{n - 1} = 0$$ 6. **Conclusion:** The limit is 0 because the denominator grows faster than the numerator.