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MATH / The set of real numbers x for which

Problem

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problem

The set of real numbers xx for which 1x−2009+1x−2010+1x−2011≥1\dfrac{1}{x-2009}+\dfrac{1}{x-2010}+\dfrac{1}{x-2011}\ge 1is the union of intervals of the form a<x≤ba<x\le b. What is the sum of the lengths of these intervals?
Plain-text mathematical notation (without MathML)
The set of real numbers x for which
(1)/(x−2009)+(1)/(x−2010)+(1)/(x−2011)≥1is the union of intervals of the form a<x≤b. What is the sum of the lengths of these intervals?
Original LaTeX notation
The set of real numbers $x$ for which
$$\dfrac{1}{x-2009}+\dfrac{1}{x-2010}+\dfrac{1}{x-2011}\ge 1$$is the union of intervals of the form $a<x\le b$. What is the sum of the lengths of these intervals?

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
b6dae4ac-7cad-5042-8bea-4ac0ae1f9c37
task_key
intermediate~5falgebra--test--b6dae4ac-7cad-5042-8bea-4ac0ae1f9c37
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import