9. ( x + 5 ) / ( x + 2 ) < 0 <=> ( x + 5 < 0 and x + 2 > 0 ) or ( x + 5 > 0 or x + 2 < 0 ) <=> ( x < -5 and x > - 2 ) or ( x > -5 and x < -2 ) <=> ( x∈Ф ) or ( - 5 < x < - 2 ) <=> - 5 < x < - 2.
[tex] \frac{x}{x+1} < \frac{x}{x-1} \\ \frac{x}{x+1} - \frac{x}{x-1} <0 \\ x( \frac{1}{x+1} - \frac{1}{x+1})<0 \\ \frac{2x}{x^2-1} <0[/tex] Consider the function and define the domain of the function [tex]y=\frac{2x}{x^2-1}[/tex] [tex]x^2-1 \neq 0 \\ x^2 \neq 1 \\ x \neq \pm 1[/tex] Function is zero [tex]\frac{2x}{x^2-1}=0 \\ 2x=0 \\ x=0[/tex]
