Indian Math Olympiad. Check out this fascinating tricks used in solving a complicated fraction.

This is an interesting video on how to solve a complicated math Olympiad fraction
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[@lechaiku]

Another approach :
x/21 + x/77 + x/165 + x/285 = 200
x/(3*7) + x(7*11) + x(15*11) +x (15*19)
We can use that trick:
Observe that the difference between both factors in each denominators is 4 (it's our D)
so, we can use the multiplication of 1/D by the difference between the smallest factor and the biggest one divided by product of ab.
a = 3; b = 19 ------> (b - a) / (ab) and D = 4 ---------------> 1/D
1/D [(b-a)/ab
x/4(19 - 3)/ 3*19 = 200
x/4(16/57) = 200
4x / 57 = 200
x = 50*57
x = 2850
This very useful concept is based on identity:
1/a - 1/b = b-a/ ab
and
1/ab = [(1/a) - (1/b)] (1/ (b-a)

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