1. The numbers $a$ and $b$ satisfy the equation $\frac{2 a}{a+b}+\frac{b}{a-b}=2$. Find all possible values of the expression $\frac{3 a-b}{a+5 b}$.
1. From the given equality, it follows that $2 a(a-b)+b(a+b)=2\left(a^{2}-b^{2}\right), b(3 b$ $-a)=0$, from which $b=0$ or $a=3 b$. Both cases are possible. If $b=0$, then the given equality holds for all $a \neq 0$, and the value of the expression $\frac{3 a-b}{a+5 b}$ for all such $a$ and $b$ is 3. If $a=3 b$ and $a$ and $b$ are non-zero, then the given equality holds, and the value of the expression $\frac{3 a-b}{a+5 b}$ for all specified $a$ and $b$ is 1.

Answer: 1 and 3.