Circuit Theory/Superposition

Goal
Split multisource circuit into smaller, simpler circuits, compute current or voltage and add.

Procedure
Pick 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
Find the current through the 3 ohm resistor assuming moving left to right is positive:

The total current in the direction shown on the original diagram is going to be: $$\frac{24}{5} - \frac{14}{5} - \frac{3}{5} = \frac{7}{5} amp$$

Example 2
Find the current through the 4 ohm resistor assuming moving left to right is positive:

$$i = 35/3 - 11/36 + 25/18 = 51/4 = 12.75 amps$$

Simulation at circuit lab confirms the answer: