Precalculus (10th Edition)

All real numbers except $-\frac{1}{2}$ and $3$.
Factor the denominator to obtain: $2x^2-5x-3=(2x+1)(x-3)$ The denominator cannot be $0$ hence, $(2x+1)(x-3)\ne0\\ \longrightarrow 2x+1\ne0, \text{ and } x-3\ne0\\ \longrightarrow x\ne-\frac{1}{2}\text{ and } x\ne3$. Therefore the domain is all real numbers except $-\frac{1}{2}$ and $3$.