jmc

We can build a sign chart:

$$\begin{array}{cccc}& x<-3& -3<x<0& 0<x\\ x+3& -& +& +\\ x& -& -& +\\ \frac{x}{x+3}& +& -& +\end{array}$$Also, $\frac{x}{x+3}=0$ for $x=0.$

Thus, the solution is $x\in \boxed{(-\infty ,-3)\cup [0,\infty )}.$