AMC 12 2010b 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} \textbf{(B)}\ \dfrac{1004}{335} \textbf{(C)}\ 3 \textbf{(D)}\ \dfrac{403}{134} \textbf{(E)}\ \dfrac{202}{67}