Find all asymptotes of a function

Find all asymptotes of a function:

$f(x)=\mathrm{log}({x}^{2}-4)$

Domain: $x\in (-\mathrm{\infty},-2)\cup (2,\mathrm{\infty})$

Vertical asymptotes are x=−2 (left) and x=2(right):

$\underset{x\to \text{}-{2}^{-}}{lim}\mathrm{log}({x}^{2}-4)=-\mathrm{\infty}$

$\underset{x\to \text{}{2}^{+}}{lim}\mathrm{log}({x}^{2}-4)=-\mathrm{\infty}$

I calculate the limits in +/- infinity:

$\underset{x\to \text{}+\mathrm{\infty}}{lim}\mathrm{log}({x}^{2}-4)=+\mathrm{\infty}$

$\underset{x\to \text{}-\mathrm{\infty}}{lim}\mathrm{log}({x}^{2}-4)=+\mathrm{\infty}$

So I'm looking for the oblique asymptotes of a form y=Ax+B:

${A}_{+}=\underset{x\to \text{}+\mathrm{\infty}}{lim}\frac{\mathrm{log}({x}^{2}-4)}{x}=\underset{x\to \text{}+\mathrm{\infty}}{lim}\frac{\frac{2x}{{x}^{2}-4}}{1}=0$

${B}_{+}=\underset{x\to \text{}+\mathrm{\infty}}{lim}\mathrm{log}({x}^{2}-4)-{A}_{+}x=+\mathrm{\infty}$

The same for $-\mathrm{\infty}$. How should I interpret this? There are no oblique asymptotes?

Find all asymptotes of a function:

$f(x)=\mathrm{log}({x}^{2}-4)$

Domain: $x\in (-\mathrm{\infty},-2)\cup (2,\mathrm{\infty})$

Vertical asymptotes are x=−2 (left) and x=2(right):

$\underset{x\to \text{}-{2}^{-}}{lim}\mathrm{log}({x}^{2}-4)=-\mathrm{\infty}$

$\underset{x\to \text{}{2}^{+}}{lim}\mathrm{log}({x}^{2}-4)=-\mathrm{\infty}$

I calculate the limits in +/- infinity:

$\underset{x\to \text{}+\mathrm{\infty}}{lim}\mathrm{log}({x}^{2}-4)=+\mathrm{\infty}$

$\underset{x\to \text{}-\mathrm{\infty}}{lim}\mathrm{log}({x}^{2}-4)=+\mathrm{\infty}$

So I'm looking for the oblique asymptotes of a form y=Ax+B:

${A}_{+}=\underset{x\to \text{}+\mathrm{\infty}}{lim}\frac{\mathrm{log}({x}^{2}-4)}{x}=\underset{x\to \text{}+\mathrm{\infty}}{lim}\frac{\frac{2x}{{x}^{2}-4}}{1}=0$

${B}_{+}=\underset{x\to \text{}+\mathrm{\infty}}{lim}\mathrm{log}({x}^{2}-4)-{A}_{+}x=+\mathrm{\infty}$

The same for $-\mathrm{\infty}$. How should I interpret this? There are no oblique asymptotes?