Answer
All real numbers; $x \ne -\frac{1}{2}, 3$
Work Step by Step
The domain of the function is all real numbers, except for when the denominator is 0. Thus, we let the denominator equal 0:
$$ 2x^2 -5x -3 = 0 \\ (2x+1)(x-3)=0\\ x = -\frac{1}{2}, 3\\ $$
Domain: All real numbers; $x \ne -\frac{1}{2}, 3$
