\(\left(x+2\right)\left(x+\frac{2}{3}\right)>0\)
(+) \(\begin{cases}x+2>0\\x+\frac{2}{3}>0\end{cases}\)\(\Rightarrow\begin{cases}x>-2\\x>-\frac{2}{3}\end{cases}\)\(\Rightarrow x>-\frac{2}{3}\)
(+) \(\begin{cases}x+2< 0\\x+\frac{2}{3}< 0\end{cases}\)\(\Rightarrow\begin{cases}x< -2\\x< -\frac{2}{3}\end{cases}\)\(\Rightarrow x< -2\)
Vậy \(x>-\frac{2}{3}\) ; \(x< -2\)