9.040. $\frac{x-7}{\sqrt{4 x^{2}-19 x+12}}<0$.

Solve the inequality $\frac{x-7}{\sqrt{4 x^{2}-19 x+12}}<0$.
## Solution.

The given inequality is equivalent to the system of inequalities

$$
\left\{\begin{array}{l}
x-70
\end{array}\right.
$$

Using the interval method, we obtain \( x \in \left(-\infty ; \frac{3}{4}\right) \cup (4 ; 7) \).

![](https://cdn.mathpix.com/cropped/2024_05_22_fa9db84b44b98ec0a5c7g-531.jpg?height=138&width=610&top_left_y=1637&top_left_x=429)

Answer: \( x \in \left(-\infty ; \frac{3}{4}\right) \cup (4 ; 7) \).