Answer
$$0$$
Work Step by Step
\begin{aligned}
\lim _{x \rightarrow-\infty}(\sqrt{x^{2}+3}+x) &=\lim _{x \rightarrow-\infty}[\sqrt{x^{2}+3}+x] \cdot\left[\frac{\sqrt{x^{2}+3}-x}{\sqrt{x^{2}+3}-x}\right]\\
&=\lim _{x \rightarrow-\infty} \frac{\left(x^{2}+3\right)-\left(x^{2}\right)}{\sqrt{x^{2}+3}-x}\\
&=\lim _{x \rightarrow-\infty} \frac{3}{\sqrt{x^{2}+3-x}} \\ &=\lim _{x \rightarrow-\infty} \frac{\frac{3}{\sqrt{x}}}{\sqrt{1+\frac{3}{x^{2}}} \frac{x}{\sqrt{x^{2}}}}\\
&=\lim _{x \rightarrow-\infty} \frac{-\frac{3}{x}}{\sqrt{1+\frac{3}{x^{2}}}+1}\\
&=\frac{0}{1+1}\\
&=0 \end{aligned}