## Task B-3.3.

Solve the inequality

$$
\frac{\tan(\pi x)-1}{\tan(\pi x)+1}>1
$$
## First solution.

Let's write the given inequality as $\frac{\operatorname{tg}(\pi x)-1}{\operatorname{tg}(\pi x)+1}-1>0$, and bring the expression on the left side to a common denominator

$$
\begin{gathered}
\frac{(\operatorname{tg}(\pi x)-1)-(\operatorname{tg}(\pi x)+1)}{\operatorname{tg}(\pi x)+1}>0 \\
\frac{-2}{\operatorname{tg}(\pi x)+1}>0
\end{gathered}
$$

From here, $-\frac{\pi}{2}+k \pi<\pi x<-\frac{\pi}{4}+k \pi, \quad k \in \mathbb{Z}$, 2 points or $-\frac{1}{2}+k<x<-\frac{1}{4}+k, \quad k \in \mathbb{Z}$.