Question:
The solution set of the inequation $\frac{|x|+1}{|x|-1}<0$ is _______________
Solution:
for $\quad \frac{|x|+1}{|x|-1}<0$
Since $|x|+1>0 \quad$ (always)
$\Rightarrow \quad|x|-1<0 \quad\left(\because \frac{|x|+1}{|x|-1}<0\right)$
i. e. $|x|<1$
i.e. $\quad-1 i.e. $x \in(-1,1)$ i. e. solution set of $\frac{|x|+1}{|x|-1}<0$ is $(-1,1)$