Advent Puzzles 2014: puzzle 15 solution

1 − 2 + 3 / 4 / 5 + 6 / 7 / 8 / 9 / 10 − 11 + 12 − 13 / 14 / 15 = 15 / 12 / 14

Some analysis:
1−2 + (3/4/5) + (6/7/8/9/10) −11+12 − (13/14/15) = 15/12/14
−1  + 3/20    + 6/5040       +1     − 13/210     = 15/168
      3/20    + 6/5040              − 13/210     = 15/168
      126/840 + 1/840               − 52/840     = 75/840
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