Evaluating $\lim\limits_{x \to \infty } \frac{5 + \sqrt{x^2+5}}{x-6}$ I don't know how to evaluate
$$\lim_{x \to \infty } \frac{5 + \sqrt{x^2+5}}{x-6}$$


*

*It is $\frac{\infty}{\infty}$

*I have tried to multiply by $5 - \sqrt{x^2+5}$, but I reach a wrong result.

*I have tried to take the derivative of $5 + \sqrt{x^2+5}$ and $x-6$, but this also doesn't help.
Probably, I should use another method. Which method do I use?

Derivative of the numerator: $(5+ \sqrt{x^2+5})'= (\sqrt{x^2+5})'= \frac{(x^2+5)'}{2}\sqrt{x^2+5}^{-1} = \frac{2x}{2 \sqrt{x^2+5}} = \frac{1}{\sqrt{1+\frac{5}{x^2}}}$.
Derivative of the denominator: $(x-6)'=1$. 
L'Hospital's rule is possible.
