Answer
Domain: All real numbers; $x \ne \frac{1}{3}, -2$
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:
$$ 3x^2 +5x -2 =0 \\ (3x-1)(x+2)=0 \\ x = \frac{1}{3}, -2\\ $$
Thus, we know that x cannot equal 1/3 or -2.
Domain: All real numbers; $x \ne \frac{1}{3}, -2$
