Answer
$(-\infty,-1)$
Work Step by Step
Step 1. Rewrite the inequality as $\frac{5}{x+1}-\frac{12}{x+1}\gt0$ or $\frac{-7}{x+1}\gt0$
Step 2. Identify the boundary point as $x=-1$
Step 3. Use test points at $x=-2, 0$, the signs of the left side are $+, -$
Step 4. The inequality requires positive (left region, excluding $x=-1$), thus the solution intervals are $(-\infty,-1)$
