Answer
(-∞, -1/2) U (-1/2, 3) U (3, ∞)
Work Step by Step
$g(x) = \frac{2x^2 + 5x + 3}{2x^2 - 5x -3}$
Domain is the set of numbers such that g(x) is defined, so find the numbers in which the denominator is equal to zero.
$2x^2 - 5x - 3 = 0$
$(2x+1) (x-3) = 0$
$x= -1/2, 3$
Thus the Domain is (-∞, -1/2) U (-1/2, 3) U (3, ∞)