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May 2009
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ALGERIA
Solve in R : \(\displaystyle \frac{1}{x-1}-\frac{4}{x-2}+\frac{4}{x-3}-\frac{1}{x-4}< \frac{1}{30}\)
 

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Solve in R : \(\displaystyle \frac{1}{x-1}-\frac{4}{x-2}+\frac{4}{x-3}-\frac{1}{x-4}< \frac{1}{30}\)
I would start by solving the corresponding equality, which will yield a quartic polynomial once you multiply through by the LCM of the denominators (you will need to solve for roots).

The roots will partition the real number line into some number of regions, and you can determine for which regions the inequality holds.