PUZZLE #4 SECOND LEG (from the 24th of February to the 11th of March 2010)

INHUMAN SIMPLIFICATION

Simplify up to the maximum this big fraction in which both numbers (numerator and denominator), have 2010 digits:

121212...121212

212121...212121


SOLUTION 
We've received 7 correct solutions from:
Zsofia Zentai (Hungary)
Reka Vass (Hungary)
Kristynna Mandá ková ( Czech Republic)
Joan Josep Pla (Spain) 
Luisa Wiechert (Germany)
Julian Kaping (Germany).
Tobias Latta (Germany)


The correct solution from LUISA WIECHERT is:
Simplify up to the maximum: 

121212...121212

212121...212121

Solution:             If you reduce this fraction by 3, you get 4040…0404/7070…0707    (2009 digits).                  
             Then you can reduce it by 1010…0101     (2009 digits)

                               and you get 4/7.

                               So the solution is 4/7.