Solving an inequality fot hyperbolas

Question

I am trying to solve:
$$\frac{1}{x-2} < \frac{1}{x+2}. $$ I think I have done so by sketching the graph, namely $-2 < x < 2 $ but I would like to see how I could have done this algebraically.

TIA

Answer 1

$$\dfrac1{x-2}<\dfrac1{x+2}\iff\dfrac{x+2-(x-2)}{(x-2)(x+2)}<0$$

So we need $(x-2)(x+2)<0\iff -2<x<2$