1. **State the problem:** Find the limit $$\lim_{x \to 0} \frac{x - 1}{x^2 - 1}$$. 2. **Recall the formula and rules:** To find limits involving rational functions, try to simplify the expression by factoring and canceling common factors if possible. 3. **Factor the denominator:** $$x^2 - 1 = (x - 1)(x + 1)$$ 4. **Rewrite the limit:** $$\lim_{x \to 0} \frac{x - 1}{(x - 1)(x + 1)}$$ 5. **Cancel the common factor:** $$\lim_{x \to 0} \frac{\cancel{x - 1}}{\cancel{x - 1}(x + 1)} = \lim_{x \to 0} \frac{1}{x + 1}$$ 6. **Evaluate the limit by direct substitution:** $$\frac{1}{0 + 1} = 1$$ **Final answer:** $$\lim_{x \to 0} \frac{x - 1}{x^2 - 1} = 1$$