9.031. $\frac{3 x^{2}-10 x+3}{x^{2}-10 x+25}>0$.
Solution.

From the condition $\frac{3\left(x-\frac{1}{3}\right)(x-3)}{(x-5)^{2}}>0 \Leftrightarrow\left\{\begin{array}{l}\left(x-\frac{1}{3}\right)(x-3)>0, \\ x \neq 5 .\end{array}\right.$

Using the number line, we get $x \in\left(-\infty ; \frac{1}{3}\right) \cup(3 ; 5) \cup(5 ; \infty)$.

![](https://cdn.mathpix.com/cropped/2024_05_22_fa9db84b44b98ec0a5c7g-528.jpg?height=124&width=470&top_left_y=1372&top_left_x=425)

Answer: $x \in\left(-\infty ; \frac{1}{3}\right) \cup(3 ; 5) \cup(5 ; \infty)$.