1. **State the problem:** Find the limit as $x$ approaches 2 of the function $$\frac{x^2 - 4}{x - 2}$$. 2. **Recall the formula and rules:** The direct substitution of $x=2$ gives $$\frac{2^2 - 4}{2 - 2} = \frac{4 - 4}{0} = \frac{0}{0}$$ which is an indeterminate form. This means we need to simplify the expression before evaluating the limit. 3. **Simplify the expression:** Factor the numerator using the difference of squares: $$x^2 - 4 = (x - 2)(x + 2)$$ 4. **Rewrite the limit:** $$\lim_{x \to 2} \frac{(x - 2)(x + 2)}{x - 2}$$ 5. **Cancel common factors:** $$\lim_{x \to 2} \frac{\cancel{(x - 2)}(x + 2)}{\cancel{(x - 2)}} = \lim_{x \to 2} (x + 2)$$ 6. **Evaluate the limit:** Substitute $x=2$: $$2 + 2 = 4$$ **Final answer:** $$\boxed{4}$$