2010 AMC 12B Problem 24

The set of real numbers x for which

\dfrac{1}{x-2009}+\dfrac{1}{x-2010}+\dfrac{1}{x-2011}\ge1

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

\textbf{(A)}\ \dfrac{1003}{335} \qquad \textbf{(B)}\ \dfrac{1004}{335} \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ \dfrac{403}{134} \qquad \textbf{(E)}\ \dfrac{202}{67}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.