9.190. $\frac{x^{3}-2 x^{2}-5 x+6}{x-2}>0$.

9.190. $\frac{x^{3}-2 x^{2}-5 x+6}{x-2}>0$.
Solution.

Rewrite the given inequality as $\frac{(x-1)(x+2)(x-3)}{x-2}>0 \Leftrightarrow$ $\Leftrightarrow(x-1)(x+2)(x-3)(x-2)>0$. Using the method of intervals, we get $x \in(-\infty ;-2) \cup(1 ; 2) \cup(3 ; \infty)$.

![](https://cdn.mathpix.com/cropped/2024_05_21_3edb7be591bff54ce350g-0693.jpg?height=85&width=438&top_left_y=1738&top_left_x=463)

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