I notice that the equation involves a rational function, which means that the domain will be all real numbers except those that make the denominator zero. To find those values, I need to solve the equation $2x^2 - 6x + 4 = 0$. I could use the quadratic formula, but I notice that this equation is easily factorable: $2x^2 - 6x + 4 = 2(x - 1)(x - 2)$. So the equation is zero when $x = 1$ or $x = 2$. These are the values of $x$ that I need to exclude from the domain, so $A = 1$ and $B = 2$. Therefore, $A + B = 1 + 2 = 3$. 
The domain of the equation $y = \frac{3x}{2x^2 - 6x + 4}$ is the set of all real numbers with the exception of the values $x = A$ and $x = B$. What is $A + B$?