Answer
$2$
Work Step by Step
In order to simplify the given expression, we will use the following rules.
$(a) \lim\limits_{x \to a} \dfrac{p(x)}{q(x)}=\dfrac{\lim\limits_{x \to a} p(x)}{\lim\limits_{x \to a} q(x)} \\ (b) \lim\limits_{x \to a} k(x)=k(a)$ ;
where $a$ is a constant.
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Thus, we have:
$$ \lim\limits_{x \to 2} \dfrac{x^2-4}{x^2-2x}=\lim\limits_{x \to 2} \dfrac{(x-2)(x+2)}{x(x-2)}\\=\dfrac{\lim\limits_{x \to 2} x+2}{\lim\limits_{x \to 2} x} \\=\dfrac{2+2}{2}\\=2$$
