smc

We hope to simplify this expression into a quadratic in order to find the solutions. To do this, we find a common denominator to the LHS by multiplying by $ab$. $$a+b=\frac{ab}{a+b}$$ $$a^2+2ab+b^2=ab$$ $$a^2+ab+b^2=0.$$ By the quadratic formula and checking the discriminant (imagining one of the variables to be constant), we see that this has no real solutions. Thus the answer is $\boxed{\text{none}}$.