1. **State the problem:** Evaluate the limit $$\lim_{x \to 1} \frac{x^2 - 1}{x - 1}$$. 2. **Recall the formula and rules:** The expression is a rational function. Direct substitution of $x=1$ gives $$\frac{1^2 - 1}{1 - 1} = \frac{0}{0}$$, which is an indeterminate form. We need to simplify the expression. 3. **Factor the numerator:** Use the difference of squares formula: $$x^2 - 1 = (x - 1)(x + 1)$$. 4. **Simplify the expression:** $$\frac{x^2 - 1}{x - 1} = \frac{(x - 1)(x + 1)}{x - 1}$$. Since $x \neq 1$ in the limit process, we can cancel $x - 1$: $$= x + 1$$. 5. **Evaluate the limit:** Substitute $x = 1$: $$1 + 1 = 2$$. **Final answer:** $$\lim_{x \to 1} \frac{x^2 - 1}{x - 1} = 2$$.