$9.249 \log _{a} \frac{1+\log _{a}^{2} x}{1-\log _{a} x}<0$.

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$9.249 \log _{a} \frac{1+\log _{a}^{2} x}{1-\log _{a} x}<0$.
Solution. Let $y=\log _{a} x$, then $\log _{a} \frac{1+y^{2}}{1-y}1, \\ \frac{1+y^{2}}{1-y}0\end{array} \Leftrightarrow\left\{\begin{array}{l}a>1, \\ y(y+1)0\end{array} \Leftrightarrow\left\{\begin{array}{l}a>1, \\ -11, \\ \frac{1}{a}1\end{array} \Leftrightarrow\left\{\begin{array}{l}0\frac{1}{a}, \\ a1$, then $x \in\left(\frac{1}{a} ; 1\right)$; if $01-x$.

Solution. The inequality is equivalent to the following:

$\left[\begin{array}{l}x^{3}-1>1-x, \\ x^{3}-10, \\ (x-1)(x+1) x1, \\ 0<x<1, \\ x<-1 .\end{array}\right.\right.\right.$

Answer: $\quad x \in(-\infty ;-1) \cup(0 ; 1) \cup(1 ;+\infty)$.