Answer
$(-\infty,-2]U(1,2)$
Work Step by Step
Step 1. Rewrite the inequality as $\frac{4}{2-x}-\frac{3}{1-x}\ge0$ or $\frac{-x-2}{(2-x)(1-x)}\ge0$
Step 2. Identify the boundary point as $x=-2,1,2,$
Step 3. Use test points at $x=-3, 0, \frac{3}{2}, 3$, the signs of the left side rational are $+, -,+,-$
Step 4. The inequality requires positive (1st and 3rd regions, excluding $x=1,2$), thus the solution intervals are $(-\infty,-2]U(1,2)$
