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