Answer
$(-\infty,-1)U(-1,4)U(4,\infty)$.
Work Step by Step
Step 1. Given $f(x)=3x^2-4$ and $g(x)=x^2-3x-4$, we can find the domain for $f$ is $(-\infty,\infty)$ and the domain for $g$ is $(-\infty,\infty)$.
Step 2. From $g(x)=0$, we have $x^2-3x-4=0$ or $(x+1)(x-4)=0$ which gives $x=-1,4$
Thus the domain for $(\frac{f}{g})(x)$ is $(-\infty,-1)U(-1,4)U(4,\infty)$.
