FORTNIGHT'S PUZZLE 7

PUZZLE 7: 7th-13th May (to be e-mailed by the 14th May)
POSTED BY IES CAMPANAR

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
The correct solution from LUISA GARCÍA is:Simplify up to the maximum:
121212...121212
212121...212121

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.