Answer
$(-3,0)\cup(2,\frac{9}{2}]$
Work Step by Step
1. move all items to one side $f(x)=\frac{1}{x-2}+\frac{2}{x+3}-\frac{3}{x}
=\frac{x^2+3x+2x^2-4x-3x^2-3x+18}{x(x-2)(x+3)}$
$f(x)=-\frac{2(2x-9)}{x(x-2)(x+3)}\geq0$
2. use cut points $-3,0,2,9/2(4.5)$ to make a table as shown.
3. Draw conclusion based on the table $(-3,0)\cup(2,\frac{9}{2}]$
