Answer
$\{x|x\ne-2,\frac{1}{3} \}$.
Work Step by Step
The domain requirement of this function is $3x^2+5x-2\ne0 \Longrightarrow (3x-1)(x+2)\ne0 \Longrightarrow x\ne-\frac{1}{2},3$ or $\{x|x\ne-2,\frac{1}{3} \}$.
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