1. **Stating the problem:** Find the limit $$\lim_{x \to 2} \frac{x^2 - 4}{x - 2}$$. 2. **Formula and rules:** The limit of a function as $x$ approaches a value $a$ is the value that the function approaches as $x$ gets closer to $a$. If direct substitution results in an indeterminate form like $\frac{0}{0}$, we simplify the expression. 3. **Intermediate work:** Substitute $x=2$ directly: $$\frac{2^2 - 4}{2 - 2} = \frac{4 - 4}{0} = \frac{0}{0}$$ which is indeterminate. 4. **Simplify the expression:** Factor the numerator: $$\frac{x^2 - 4}{x - 2} = \frac{(x - 2)(x + 2)}{x - 2}$$ 5. **Cancel common factors:** $$\frac{\cancel{(x - 2)}(x + 2)}{\cancel{(x - 2)}} = x + 2$$ 6. **Evaluate the limit:** Now substitute $x=2$: $$2 + 2 = 4$$ 7. **Answer:** Therefore, $$\lim_{x \to 2} \frac{x^2 - 4}{x - 2} = 4$$. This shows how to handle limits that initially give an indeterminate form by factoring and simplifying.