Question

The solution set of the inequation $\frac{\left|x\right|+1}{\left|x\right|-1}<0$ is ___________.

Answer 1

$$\begin{gathered} \mathrm{for}\frac{\left|x\right|+1}{\left|x\right|-1}<0 \\ \mathrm{Since}\left|x\right|+1>0\left(\mathrm{always}\right) \\ \Rightarrow \left|x\right|-1<0\left(\because \frac{\left|x\right|+1}{\left|x\right|-1}<0\right) \\ \mathrm{i}.\mathrm{e}.\left|x\right|<1 \\ \mathrm{i}.\mathrm{e}.-1<x<1 \\ \mathrm{i}.\mathrm{e}.x\in (-1,1) \\ \mathrm{i}.\mathrm{e}.\mathrm{solution}\mathrm{set}\mathrm{of}\frac{\left|x\right|+1}{\left|x\right|-1}<0\mathrm{is}(-1,1) \end{gathered}$$