Limits of a Function easy

Theorem:

Let $f\left( x \right) =\dfrac { g\left( x \right) }{ h\left( x \right) }$ be a function for $x \in \mathbb{Z}$ (for this question, else the above is a rational function), if: $g(a)\neq 0$ and $h(a) = 0$ then the $\lim _{ x\rightarrow a }{ f\left( x \right) }$ does not exist

Now let $g(x)=x^2-9$ and $h(x)=x+4$ then solve the question for $f(x)=\dfrac{g(x)}{h(x)}$ .

Well the given it diverge.