Finding the current through a resistor using superposition theorem.

1. The problem statement, all variables and given/known data
We have this circuit.


The problem states to find i, or the current through the 3 ohm resistor.

2. Relevant equations
V = IR


3. The attempt at a solution

I've started by shorting out both voltage sources and leaving only the current source in the circuit. I paralleled the 4ohm resistor and the 3ohm resistor nearest the current source to get 12/7 ohms equivalent resistance. Multiplying that by 3A gives me 5.1 volts going through the 4 ohm resistor nearest the current source and 5.1 volts going through the 3 ohm resistor.

Dividing 5.1 volts by 3ohms gives me 1.7A going through the 3 ohm resistor from the current source alone. I'm not sure if did that right and need some help on what to do.

 

Ahh I should have clarified that I was going to solve it again with the other sources still there while the current source becomes an open circuit. I guess my real question was if I got the right amount of current through the 3 ohm resistor using the current source alone, which that will be added to the other currents I get when using the seperate voltage sources alone.