Answer
$(-3, -5/2] U [5/2, 3) $
Work Step by Step
$\frac{4x^2 - 25}{x^2 - 9} \leq 0$
Find the zeros of the expressions in the numerator AND the denominator
$(2x + 5) (2x - 5) = 0$; $(x-3)(x+3) = 0$
$x = -5/2, 5/2, 3, -3$
Test numbers in between those zero values to determine if the function is negative or positive
(-∞, -3) $\frac{(-)(-)}{(-)(-)} = (+)$
(-3, -5/2] $\frac{(-)(-)}{(-)(+)} = (-)$
[-5/2, 5/2] $\frac{(+)(-)}{(-)(+)} = (+)$
[5/2, 3) $\frac{(+)(+)}{(-)(+)} = (-)$
(3, ∞) $\frac{(+)(+)}{(+)(+)} = (+)$
Thus the solution is $(-3, -5/2] U [5/2, 3) $