9.3. The numbers $a$ and $\mathrm{b}$ satisfy the equation $\frac{2 a}{a+b}+\frac{b}{a-b}=2$. Find all possible values of the expression $\frac{3 a-b}{a+5 b}$.
Solution. From the given inequality, it follows that

$$
2 a(a-b)+b(a+b)=2\left(a^{2}-b^{2}\right) \quad b(3 b-a)=0
$$

From which $\mathrm{b}=0$ or $\mathrm{a}=3 \mathrm{~b}$. If $\mathrm{b}=0$, then the given equality holds for all $a \neq 0$, which means the expression $\frac{3 a-b}{a+5 b}=3$.

If $a=3 b$ and $\mathrm{a}$ and $\mathrm{b}$ are different from zero, then $\frac{3 a-b}{a+5 b}=1$.