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Let
$$A = \left\{ x \in \mathbb R \;\; \text{such that} \;\; \dfrac 1 {x - 1} + \dfrac 2 {x-2} + ... + \dfrac {57} {x-57} \ge 3 \right\}$$
One can prove that \(A\) a an union of intervals. Find the sum of the lengths of the intervals \(A\) is made of.
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