Solve the following system of equations:

$$
\begin{gathered}
\frac{x}{a-2 b}-\frac{y}{a+2 b}=\frac{6 a b}{a^{2}-4 b^{2}} \\
\frac{x+y}{a+2 b}+\frac{x-y}{a-2 b}=\frac{2\left(a^{2}-a b+2 b^{2}\right)}{a^{2}-4 b^{2}}
\end{gathered}
$$
Removing the denominators:

$$
\begin{gathered}
x(a+2 b)-y(a-2 b)=6 a b \\
(x+y)(a-2 b)+(x-y)(a+2 b)=2\left(a^{2}-a b+2 b^{2}\right)
\end{gathered}
$$

From (4),

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

Substituting this into (3), we get

$$
y=\frac{a^{3}-5 a^{2} b+4 b^{3}}{a^{2}-4 a b-4 b^{2}}=a-b
$$

Substituting this value of $y$ into (5):

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

(József Szabó, Kecskemét.)

The problem was solved by: Bayer B., Bárdos Gy., Csete A., Dolowschiák M., Faith F., Filkorn J., Freibauer E., Kárf J., Kornis Ö., Krausz B., Krisztián Gy., Lindtner M., Lukhaub Gy., Obláth R., Oltay K., Perl Gy., Pethő J., Póka Gy., Pollák M., Rehberger Z., Sasvári G., Sasvári J., Stromfeld F., Szibelth S., Szokolay L., Tinyó J., Weisz J.