5. Solve the inequality $2 x-1>\frac{3}{2 x+1}$.
Solution:

$$
2 x-1>\frac{3}{2 x+1} ; 2 x-1-\frac{3}{2 x+1}>0
$$

$$
\frac{4 x^{2}-1-3}{2 x+1}>0 ; \frac{4(x-1)(x+1)}{2 x+1}>0
$$

![](https://cdn.mathpix.com/cropped/2024_05_06_8eeeb8d6ace591217257g-14.jpg?height=197&width=737&top_left_y=1866&top_left_x=1205)

Answer: $\left(-1 ;-\frac{1}{2}\right) \cup(1 ;+\infty)$.