Solve the following equation:

$$
\frac{x+a+b}{x+a}=\frac{x+a-b}{x-a}-\frac{a^{2}+b^{2}}{x^{2}-a^{2}}
$$
Our equation can also be written as:

$$
(x+a)(x+a-b)-(x-a)(x+a+b)=a^{2}-b^{2}
$$

or

$$
2 a x-2 b x=b^{2}-a^{2},
$$

from which

$$
x=\frac{b^{2}-a^{2}}{2(a-b)}=-\frac{a+b}{2} .
$$

(Kuffler Albert, Budapest.)