Answer
$(-7, -5/2] U (5, ∞) $
Work Step by Step
$\frac{2x+5}{x^2 +2x - 35} \geq 0$
Find the zeros of the expressions in the numerator AND the denominator
$2x + 5 = 0$; $(x+7)(x-5) = 0$
$x = -5/2, -7, 5$
Test numbers in between those zero values to determine if the function is negative or positive
(-∞, -7) $\frac{(-)}{(-)(-)} = (-)$
(-7, -5/2] $\frac{(-)}{(+)(-)} = (+)$
[-5/2, 5) $\frac{(+)}{(+)(-)} = (-)$
(5, ∞) $\frac{(+)}{(+)(+)} = (+)$
Thus the solution is $(-7, -5/2] U (5, ∞) $
