How does active transport help a nerve cell maintain it resting potential?

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How does active transport help a nerve cell maintain it resting potential?
The reason for the RMP is a difference in concentration of ions across the cell membrane. Outside the membrane is a high concentration of sodium ions. Inside the cell is a concentration potassium ions. Both ions carry a +1 charge. There are more sodium ions outside the cell than potassium in the cell. So there is a greater positive charge outside than inside. This difference is the voltage, in fact a voltage is defined as a potential difference. Now if the cell were to just sit there eventually a sodium will find its way into the cell through the membrane. And a potassium will find its way out of the cell through the membrane. This process is simple diffusion. Eventually both sides of the membrane would contain equal numbers of +1 charges, there would be no difference and the RMP would be zero. The sodium/potassium pump uses ATP energy to pump out 3 sodiums that find there way into the cell and pump in 2 potassium ions that have found their way out of the cell. In doing this the sodium/potassium pump maintains the difference or maintains an imbalance of ionic charge across the membrane and maintains the RMP.