Solve the following system of equations:

$$
\begin{aligned}
& \frac{1}{x-y}+\frac{1}{x+y}=a \\
& \frac{1}{x-y}-\frac{1}{x+y}=b
\end{aligned}
$$
By adding the two equations:

$$
\frac{2}{x-y}=a+b, \quad x-y=\frac{2}{a+b}
$$

By subtracting the lower from the upper:

$$
\frac{2}{x+y}=a-b, \quad x+y=\frac{2}{a-b}
$$

From $1^{\circ}$ and $2^{\circ}$

$$
x=\frac{1}{a+b}+\frac{1}{a-b}=\frac{2 a}{a^{2}-b^{2}}
$$

and

$$
y=\frac{1}{a-b}-\frac{1}{a+b}=\frac{2 b}{a^{2}-b^{2}} .
$$

(Hermann Szóllós, Esztergom.)

Number of solutions: 26.