Let's say, $a,b,c$ are three different positive integers of a single digit. $$(x-a)(x-b)+(x-b)(x-c)=0$$ What is the maximum value of the sum of the two solutions of the above equation? Write the answer in the term of $\frac {a}{b}$ so that $a$ and $b$ are coprime. What is the value of $a+b$?