23. Ta có:
$\dfrac{2}{x-1}+\dfrac{3}{x+1}<\dfrac{1}{x+2}$
$\Leftrightarrow \dfrac{5x-1}{(x-1)(x+1)}<\dfrac{1}{x+2}$
$\Leftrightarrow \dfrac{4x^2+9x-1}{(x-1)(x+1)(x+2)}<0$
$\Leftrightarrow \left[\begin{array}{l}-2<x<-1\\\dfrac{1}{8}(\sqrt{97}-9)<x<1\\x<\dfrac{1}{8}(-9-\sqrt{97})\end{array}\right.$