$\Leftrightarrow x+3>3\sqrt{x+1}\Leftrightarrow\begin{cases} x\geq -1\\ (x+3)^2>9(x+1)\end{cases}$
$\Leftrightarrow \begin{cases} x\geq -1\\ x^2-3x>0\end{cases}\Leftrightarrow\left[\begin{array}{I} –1\leq x<0\\ x>3\end{array}\right.$
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