原式= a?2 (a?1)(a+1) ÷[ (a?1)(a+1) a+1 - 2a?1 a+1 ]= a?2 (a?1)(a+1) ÷ a2?1?2a+1 a+1 = a?2 (a?1)(a+1) ? a+1 a(a?2) = 1 a(a?1) = 1 a2?a ，∵a是方程x2-x=2014的解，∴a2-a=2014，∴原式= 1 2014 ．
