jmc

The equation is well-defined unless the denominator of the given expression is equal to $0$, that is $2x^2-6x+4=0$. Factoring, $2(x-1)(x-2)=0⟹x=1,2$. Hence, $A+B=\boxed{3}$.

(We can also use Vieta's formulas, which states that the sum of the roots of the equation $a{x}^2+bx+c=0$ is $-b/a$.)