## College Algebra 7th Edition

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