Question 24
The set of real numbers $x$ for which $$
\begin{aligned} &\frac{1}{x-2009}+\frac{1}{x-2010} \\ &\quad {}+\frac{1}{x-2011}\ge1 \end{aligned}
$$ is the union of intervals of the form $a\lt x\le b.$ What is the sum of the lengths of these intervals?
\begin{aligned} &\frac{1}{x-2009}+\frac{1}{x-2010} \\ &\quad {}+\frac{1}{x-2011}\ge1 \end{aligned}
$$ is the union of intervals of the form $a\lt x\le b.$ What is the sum of the lengths of these intervals?