Answer:
-4 < x < -1 ∪ -1 < x ≤ 1
Step-by-step explanation:
The expression can be simplified, with a restriction.
[tex]\dfrac{x^2-1}{s^2+5x+4}\le0\\\\\dfrac{(x+1)(x-1)}{(x+1)(x+4)}\le 0\\\\\dfrac{x-1}{x+4} \le 0\qquad x\ne-1[/tex]
This has a zero at x=1 and a vertical asymptote at x=-4. The function changes sign at both of these values of x. The rational function will be negative where the factors have different signs, between -4 and +1. The solution must exclude x = -1.
-4 < x < -1 ∪ -1 < x ≤ 1
