\(=\lim\limits_{x\rightarrow3}\dfrac{\left(\sqrt{3x+1}-4\right)\left(\sqrt{3x+1}+4\right)\left(3+\sqrt{x+4}\right)}{\left(3-\sqrt{x+4}\right)\left(3+\sqrt{x+4}\right)\left(\sqrt{3x+1}+4\right)}\)
\(=\lim\limits_{x\rightarrow5}\dfrac{3\left(x-5\right)\left(3+\sqrt{x+4}\right)}{-\left(x-5\right)\left(\sqrt{3x+1}+4\right)}=\lim\limits_{x\rightarrow5}\dfrac{3\left(3+\sqrt{x+4}\right)}{-\left(\sqrt{3x+1}+4\right)}\)
\(=\dfrac{3.6}{-8}=-\dfrac{9}{4}\)