Solve the following equation:

$$
\log \left[\frac{1}{x}+\frac{96}{x^{2}\left(x^{2}-1\right)}\right]=\log (x+1)+\log (x+2)+\log (x+3)-2 \log x-\log \left(x^{2}-1\right)
$$
Our equation can also be written as:

$$
\frac{1}{x}+\frac{96}{x^{2}\left(x^{2}-1\right)}=\frac{(x+1)(x+2)(x+3)}{x^{2}\left(x^{2}-1\right)}
$$

or, after rearranging:

$$
x^{2}+2 x=15
$$

from which

$$
x_{1}=3, x_{2}=-5
$$

(Julius Weber, Beszterczebánya.)

The problem was also solved by: Z. Harsányi, P. Heimlich, Gy. Jánosy, J. Kiss, E. Makó, Sarolta Petrik, S. Pichler, E. Sárközy, Gy. Schlesinger, Gy. Schwarz, Gy. Schuster, I. Szécsi, D. Szőke, B. Tóth.