Answer
$(-4,-1)\cup[2,\infty)$
Work Step by Step
Step 1. Rewrite the inequality as $\frac{1}{x+1}-\frac{2}{x+4}\leq0$, $\frac{x+4-2x-2}{(x+1)(x+4)}\leq0$, $\frac{-x+2}{(x+1)(x+4)}\leq0$, and $\frac{x-2}{(x+1)(x+4)}\geq0$; then graph the function $f(x)=\frac{x-2}{(x+1)(x+4)}$ as shown in the figure.
Step 2. We can identify a zero as $x=2$, asymptotes as $x=-4$ and $x=-1$
Step 3. We can identify the regions where $f(x)\geq0$ as $(-4,-1)\cup[2,\infty)$
