Evaluate \( \lim_{x \to 2} (x^2 - 4)/(x - 2) \).

To evaluate the limit ( \lim_{x \to 2} \frac{x^2 - 4}{x - 2} ), start by recognizing that direct substitution of ( x = 2 ) yields an indeterminate form ( \frac{0}{0} ), since both the numerator and denominator equal zero when ( x = 2 ).

Next, notice that the expression in the numerator, ( x^2 - 4 ), can be factored. Using the difference of squares, we rewrite it as ( (x - 2)(x + 2) ). This allows us to simplify the limit expression:

[

\frac{x^2 - 4}{x - 2} = \frac{(x - 2)(x + 2)}{x - 2}

]

As long as ( x \neq 2 ), we can cancel the ( (x - 2) ) terms:

[

\frac{(x - 2)(x + 2)}{x - 2} = x + 2

]

Now, we can safely compute the limit as ( x ) approaches 2:

[

\lim_{x