## Precalculus (10th Edition)

All real numbers except $-2$ and $\frac{1}{3}$.
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 $\frac{1}{3}$.