A function whose graph has vertical asymptotes at $x=+2$ and $x=-2$, and a horizontal asymptote at $y=0$

Question

Determine a function whose graph has vertical asymptotes at $x=+2$ and $x=-2$, and a horizontal asymptote at $y=0$?

I don't know to satisfy these conditions.

Answer 1

$$\frac{1}{(x+2)(x-2)}$$

Can you see why it works?

Answer 2

There are countless examples of such functions: $$f(x)=\begin{cases}c\cdot\tan^k\bigg(\dfrac\pi4x\bigg),\qquad x\in(-2,2)\\\\\dfrac a{(x+2)^n},~\qquad\qquad~ x<-2\\\\\dfrac b{(x-2)^p},~\qquad\qquad~ x~>~2\end{cases}\qquad\qquad\qquad\qquad\qquad\begin{align}&a,b,c\in\mathbb R^*\\\\&k,n,p\in\mathbb N^*\end{align}$$