smc

First, note that $a\ne 0$ and $a\ne -b$. Cross multiply both sides to get $$a^2+2ab+b^2=ab$$ Subtract both sides by $ab$ to get $$a^2+ab+b^2=0$$ From the quadratic formula, $$a=\frac{-b\pm \sqrt{b^2-4b^2}}{2}$$ $$a=\frac{-b\pm \sqrt{-3b^2}}{2}$$ If $b$ is real, then $\sqrt{-3b^2}$ is imaginary because $-3b^2$ is negative. If $b$ is not real, where $b=m+ni$ and $n\ne 0$, then $\sqrt{-3b^2}$ evaluates to $\sqrt{-3m^2-6mni+3n^2}$. As long as $m\ne 0$, the expression can also be imaginary because a real number squared will be a real number. From these two points, the answer is $\boxed{\text{one real, one not real or both not real}}$.