Since $\frac{a+b}{a-b}=3$, then $a+b=3(a-b)$ or $a+b=3a-3b$. Thus, $4b=2a$ and so $2b=a$ or $2=\frac{a}{b}$. (Note that $b \neq 0$, since otherwise the original equation would become $\frac{a}{a}=3$, which is not true.)