9.154. $\frac{2-x}{x^{3}+x^{2}}>\frac{1-2 x}{x^{3}-3 x^{2}}$.
## Solution.

Rewrite the given inequality as $\frac{2-x}{x^{2}(x+1)}-\frac{1-2 x}{x^{2}(x-3)}>0 \Leftrightarrow$ $\Leftrightarrow \frac{(2-x)(x-3)-(1-2 x)(x+1)}{x^{2}(x+1)(x-3)}>0, \frac{x^{2}+6 x-7}{x^{2}(x+1)(x-3)}>0, \frac{(x+7)(x-1)}{x^{2}(x+1)(x-3)}>0 \Leftrightarrow$ $\Leftrightarrow x^{2}(x+1)(x-3)(x+7)(x-1)>0$. Using the interval method, we get $x \in(-\infty ;-7) \cup(-1 ; 0) \cup(0 ; 1) \cup(3 ; \infty)$.

![](https://cdn.mathpix.com/cropped/2024_05_21_3edb7be591bff54ce350g-0673.jpg?height=97&width=490&top_left_y=1728&top_left_x=429)

Answer: $x \in(-\infty ;-7) \cup(-1 ; 0) \cup(0 ; 1) \cup(3 ; \infty)$.