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?

Hint:
$$\frac{5+\sqrt{x^2+5}}{x-6}=\frac{\frac{5}{x}+\sqrt{\frac{x^2}{x^2}+\frac{5}{x^2}}}{\frac{x}{x}-\frac{6}{x}}=\frac{\frac{5}{x}+\sqrt{1+\frac{5}{x^2}}}{1-\frac{6}{x}}$$
$$\lim_{x\to\infty}\frac{\frac{5}{x}+\sqrt{1+\frac{5}{x^2}}}{1-\frac{6}{x}}=\frac{0+\sqrt{1+0}}{1-0}=1$$
