Prove that $\dfrac {1} {x^2-2}$ is continuous.
I first did $\left|\dfrac {1} {x^2-2} - \dfrac {1} {x_0^2-2}\right|$. Then I combined into a single fraction and was able to separate it into
$$|x-x_0|\left(\frac {|x_0|} {(x^2-2)(x_0^2-2)}+\frac {|x|} {(x^2-2)(x_0^2-2)}\right)$$
However, I do not know how to proceed.