AMC 12B 2010 Problem 24

The set of real numbers x for which

\dfrac{1}{x-2009}+\dfrac{1}{x-2010}+\dfrac{1}{x-2011} \geq 1

is the union of intervals of the form a<x \leq b. What is the sum of the lengths of these intervals?

Answer Choices
A. \dfrac{1003}{335}
B. \dfrac{1004}{335}
C. 3
D. \dfrac{403}{134}
E. \dfrac{202}{67}