To find the values of $x$ for which the equation is not defined, we need to find the values of $x$ that make the denominator equal to zero. 
The denominator of the fraction is $2x^2 - 6x + 4$. 
We can factor this as $2(x^2 - 3x + 2) = 2(x - 2)(x - 1)$. 
So, the equation is not defined when $x - 2 = 0$ or $x - 1 = 0$, which means $x = 2$ or $x = 1$. 
Therefore, the sum of $A$ and $B$ is $2 + 1 = \boxed{3}$. 
The answer is: 3
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
The equation $y = \frac{3x}{2x^2 - 6x + 4}$ is defined for all real numbers except for $x = A$ and $x = B$. What is the sum of $A$ and $B$?

### Answer:
