1. State the problem: Evaluate the limit $\lim_{x\to 2} \frac{x^2-4}{x-2}$. 2. Identify the type of limit: Plugging in $x=2$ gives an indeterminate form $\frac{0}{0}$. 3. Use the algebra rule (factor first): $$ \frac{x^2-4}{x-2}=\frac{(x-2)(x+2)}{x-2} $$ 4. Cancel the common factor (show the canceled line): $$ \frac{(x-2)(x+2)}{x-2}=\frac{\cancel{(x-2)}(x+2)}{\cancel{x-2}}=x+2 $$ 5. Now substitute the limit value: $$ \lim_{x\to 2} \left(x+2\right)=2+2=4 $$ 6. Final answer: $\boxed{4}$.