Answer
All real numbers except $-2$ and $\frac{1}{3}$.
Work Step by Step
Factor the denominator to obtain:
$3x^2+5x-2=(3x-1)(x+2)$
The denominator cannot be $0$. Hence,
$(3x-1)(x+2)\ne0\\
\longrightarrow 3x-1\ne0 \text{ and } x+2\ne0\\
\longrightarrow x\ne\frac{1}{3} \text{ and } x \ne -2$
Therefore, the domain is all real numbers except $-2$ and $\frac{1}{3}$.
