The solution set of the inequation

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 $(-1,1)$

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