[tex]\left(\dfrac{g}{f}\right)(x)=\dfrac{f(x)}{g(x)}[/tex]
[tex]\text{We have}\ f(x)=3x^2+x^4+2\ \text{and}\ g(x)=4x-3[/tex]
[tex]\text{Substitute:}\\\\\left(\dfrac{f}{g}\right)(x)=\dfrac{3x^2+x^4+2}{4x-3}[/tex]
[tex]\text{The domain:}\\\\4x-3\neq0\qquad\text{add 3 to both sides}\\\\4x\neq3\qquad\text{divide both sides by 4}\\\\x\neq\dfrac{3}{4}[/tex]
[tex]Answer:\ \boxed{\text{Domain is the set of all real numbers except}\ \dfrac{3}{4}}\\\\\boxed{D=\mathbb{R}-\left\{\dfrac{3}{4}\right\}}[/tex]
