`x≠-1`
`a)` `{3x}/{x+1}≥ 0`
$⇔\left[\begin{array}{l}\begin{cases}3x≥0\\x+1>0\end{cases}\\\begin{cases}3x≤0\\x+1<0\end{cases}\end{array}\right.$
$⇔\left[\begin{array}{l}\begin{cases}x≥0\\x>-1\end{cases}\\\begin{cases}x≤0\\x<-1\end{cases}\end{array}\right.$$⇔\left[\begin{array}{l}x≥0\\x<-1\end{array}\right.$
Vậy `x≥0` hoặc `x<-1`
`b)``{3x}/{x+1}≤ 0`
$⇔\left[\begin{array}{l}\begin{cases}3x≥0\\x+1<0\end{cases}\\\begin{cases}3x≤0\\x+1>0\end{cases}\end{array}\right.$
$⇔\left[\begin{array}{l}\begin{cases}x≥0\\x<-1\end{cases}\\\begin{cases}x≤0\\x>-1\end{cases}\end{array}\right.$$⇔-1<x≤0$
Vậy `-1<x≤0`
