Here...have some fun...
Take one of your MP3's an convert it to a WAV file. Open in up in a sound editor (SoundForge...if that still exists). Go from Stereo to Mono, back to Stereo so you know have a left & right channel with the same waveforms. Next, phase shift(or flip) one of the channels 180 degrees.
Now put your L & R speakers close together and hit play. You will notice that the sound "feels" muted. Of course, this will come no where near 100% cancellation, and it depends on your speakers and where you are in position to them.
BTW, it would be nearly impossible to record the sound of your fan with a mic, shift the signal and replay it to cancel the noice becuase of the delay in processing the signal. You would probably end up making 2x as much noise as before.