9.186. $\frac{x^{3}+3 x^{2}-x-3}{x^{2}+3 x-10}<0$.

9.186. $\frac{x^{3}+3 x^{2}-x-3}{x^{2}+3 x-10}<0$.
## Solution.

Let's rewrite the given inequality as

$$
\begin{aligned}
& \frac{\left(x^{3}-x\right)+\left(3 x^{2}-3\right)}{(x+5)(x-2)}<0 \Leftrightarrow \frac{x\left(x^{2}-1\right)+3\left(x^{2}-1\right)}{(x+5)(x-2)}<0, \frac{\left(x^{2}-1\right)(x+3)}{(x+5)(x-2)}<0 \\
& (x-1)(x+1)(x+3)(x+5)(x-2)<0 . x \in(-\infty ;-5) \cup(-3 ;-1) \cup(1 ; 2)
\end{aligned}
$$

![](https://cdn.mathpix.com/cropped/2024_05_21_3edb7be591bff54ce350g-0692.jpg?height=83&width=410&top_left_y=516&top_left_x=477)

Answer: $x \in(-\infty ;-5) \cup(-3 ;-1) \cup(1 ; 2)$.