9. $-2 \pm \sqrt{10}$.

The original equation is transformed into
$$\frac{1}{(x+2)(x-1)}+\frac{1}{(x+2)(x+5)}=2,$$

which simplifies to $x^{2}+4 x-6=0$, solving for $x$ yields $x=-2 \pm \sqrt{10}$.
Upon verification, the two roots of the original equation are $x=-2 \pm \sqrt{10}$.