Answer
$(-\infty,-2),(-1,-2/3]$
Work Step by Step
1. move all terms to one side: $\frac{1}{x}+\frac{1}{x+1}-\frac{2}{x+2}
=\frac{x^2+3x+2+x^2+2x-2x^2-2x}{x(x+1)(x+2)}=\frac{3x+2}{x(x+1)(x+2)}$
$\frac{3x+2}{x(x+1)(x+2)}\lt0$
2. Identify cut points and make a sign table as shown.
3. The solution is $(-\infty,-2),(-1,-2/3]$
