Circuit Theory/Superposition
Goal
editSplit multisource circuit into smaller, simpler circuits, compute current or voltage and add.
Procedure
editPick one source, turn off all or set to zero all others:
 Set Voltage Sources to V=0, doesn't care about current so is a short
 Set Current Sources to I=0, doesn't care about the voltage so turns into an open
Example 1
editFind the current through the 3 ohm resistor assuming moving left to right is positive:

The original circuit is equal to

this circuit where i = 24/5 plus

this circuit where i = 14/5 (current divider) plus

this circuit where i = 3/5.
The total current in the direction shown on the original diagram is going to be:
Example 2
editFind the current through the 4 ohm resistor assuming moving left to right is positive:

The original circuit is equal to

this circuit which can be redrawn as

this circuit where i = 35/3 = 11.67 plus

this circuit which can be redrawn as

this circuit where i = 11/36 = .3056 plus

this circuit which can be redrawn as

this circuit where i = 25/18 = 1.3889 (current divider)
Simulation at circuit lab confirms the answer: