#### Answer

the domain is: $\{x|x\neq-\frac{1}{2}$ and $x\neq 3\}$

#### Work Step by Step

We are given:
$g(x)= \frac{2x^{2}+5x+3}{2x^{2}-5x-3}$
We factor:
$\frac{2x^{2}+5x+3}{(2x+1)(x-3)}$
We know that the denominator can not equal 0:
$2x+1\ne 0$
$x\ne -\frac{1}{2}$
$x-3\ne 0$
$x\ne 3$
Therefore, the domain is: $\{x|x\neq-\frac{1}{2}$ and $x\neq 3\}$.