[T3] Fan Belts

[J. Jonik]

The Muir book has a line that says a shiny fan belt will slip...as mine seems to do once in a while.

Question:   Would a little sandpaper solve the shiny problem?  
Or, if part of the problem is accumulation, over time, of blown in oil, could the belt be cleaned with, maybe, some gasoline followed by a good rub with Mechanic's hand cleaner, then a rinse?

Or are belts so cheap and easy to find that all that's not worth the trouble?