If r + 1/r = 2007 + 1/2007 and s + 1/s = 2006 + 1/2006, then find the largest possible value of r - s.
Your question is vague !
If: [2007 + 1/2007] - [2006 + 1/2006] =0.99999975161709689069314229707489 . Is that what you meant?