MHB Solve Limit with Square Root: \[\lim_{x\rightarrow -\infty }\sqrt{x^{2}+3}+x\]

[Yankel]

Hello

I am trying to solve this limit here:

\[\lim_{x\rightarrow -\infty }\sqrt{x^{2}+3}+x\]

I understand that it should be 0 since the power and square root cancel each other, while the power turned the minus into plus, and then when I add infinity I get 0. This is logic, I wish to know how to show it technically, if possible.

Thank you.

 

[Greg]

Multiply by $\frac{\sqrt{x^2+3}-x}{\sqrt{x^2+3}-x}$.

 

[Yankel]

Thank you, I didn't see it.