Answer
$(-\infty,-5)U(-3,-1)$
Work Step by Step
Step 1. Rewrite the inequality as $\frac{4}{x+1}-\frac{2}{x+3}\lt0$ or $\frac{2x+10}{(x+1)(x+3)}\lt0$
Step 2. Identify the boundary point as $x=-5,-3,-1$
Step 3. Use test points at $x=-6, -4,-2,0$, the signs of the left side rational are $-,+,-,+$
Step 4. The inequality requires negative (1st and 3rd regions), thus the solution intervals are $(-\infty,-5)U(-3,-1)$
