ĐKXĐ: $\dfrac{4x+3}{x+1}\geq 0\Leftrightarrow \left\{\begin{matrix}4x+3\geq 0\\ x+1>0\end{matrix}\right. \ or \ \left\{\begin{matrix}4x+3\leq 0\\ x+1<0\end{matrix}\right.$
$\Leftrightarrow \left\{\begin{matrix}x\geq \dfrac{-3}{4}\\ x>-1\end{matrix}\right. \ or \ \left\{\begin{matrix}x\leq \dfrac{-3}{4}\\ x<-1\end{matrix}\right.\Leftrightarrow x\geq \dfrac{-3}{4} \ or \ x<-1$