Trouble understanding when voltages get split
Just re-draw the schematic, slightly:







simulate this circuit &ndash; Schematic created using CircuitLab

(Note that your confusion about "Would the 9V be split between these two resistors?" completely dissolves away by re-drawing the schematic in this modest way. And also note that I didn't actually change any meaning by doing so.)

Assuming the \$V_+\$ input neither draws nor sinks any current, you know easily how to compute \$V_+\$. It's a dead-trivial resistor-divider calculation.

Similarly, you know that the opamp (assuming it has access to the needed voltage rails) output will be adjusted such that \$V_-=V_+\$.

So it should be dead-easy to compute \$I_3\$ and \$I_4\$ (their signs not necessarily the same) and therefore \$I_5\$. Since you know the value of \$V_-\$ and the voltage drop across \$R_5\$, it's very easy to work out what \$V_\text{O}\$ must be.