1. The solution set of the inequality $\frac{x}{\sqrt{1+x^{2}}}+\frac{1-x^{2}}{1+x^{2}}>0$ is
$\qquad$
1. $\left\{x \left\lvert\, x>-\frac{\sqrt{3}}{3}\right.\right\}$.

Let $x=\operatorname{tg} \alpha, -\frac{\pi}{2} < \alpha < \frac{\pi}{2}$. Then, we have:
$$
2 \sin ^{2} \alpha-\sin \alpha-1-\frac{\sqrt{3}}{3} \cos \alpha > 0.
$$

Rearranging, we get $2 \sin ^{2} \alpha-\sin \alpha-1-\frac{\sqrt{3}}{3}$
which means $x>-\frac{\sqrt{3}}{3}$.