Solving Circuit Diagrams: 2 Batteries, Resistor & Subtraction

[majormaaz]

Just doing a couple circuit diagrams, and my brain seems to have shorted: If you have two batteries, but they're oriented where their negative terminals are facing each other (+ -) (- +) and there's a resistor in between the two batteries, could I still resolve the two batteries by subtracting the smaller battery from the larger one?

 

[mfb]

Sure, as long as you don't forget the resistor in the circuit afterwards. The position of a resistor does not matter in a series of circuit elements.