Answer
$\frac{8}{p^2+2p}\gt1$
$8\gt1(p^2+2p)$
$8\gt p^2+2p$
$0\gt p^2+2p-8$
$0\gt(p+4)(p-2)$
$-4\lt p\lt 2$
But $p$ can not be$-2\lt p\lt0$
Thus:
$-4\lt p\lt -2$
$0\lt p\lt2 $
Work Step by Step
Step 1: Multiply with $(p^2+2p)$ on both sides of the inequality
Step 2: Distribute the $1$ into the brackets
Step 3: Subtract $8$ from both sides of the inequality
Step 4: Factorize inequality (quadratic trinomial)
Step 5: substitute $p$ values in original inequality to test.
Step 6: notice the restriction, where inequality will not be true is $-2\lt p\lt0$
