Answer
$[-2.0)\cup(1,3]$
Work Step by Step
1. Move all items to one side: $f(x)=\frac{6}{x-1}-\frac{6}{x}-1\geq0$
$\frac{6x-6x+6-x^2+x}{x(x-1)}=\frac{-(x-3)(x+2)}{x(x-1)}\geq0$
2. Cut points $-2,0,1,3$, build up a sign table as shown.
3. Solutions $[-2.0)\cup(1,3]$