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Question Number 154051 by mathdanisur last updated on 13/Sep/21
let  a≠b ; b≠c and c≠a  find the minimum value of  S = ∣(a/(b-c))∣ + ∣(b/(c-a))∣ + ∣(c/(a-b))∣
$$\mathrm{let}\:\:\mathrm{a}\neq\mathrm{b}\:;\:\mathrm{b}\neq\mathrm{c}\:\mathrm{and}\:\mathrm{c}\neq\mathrm{a} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\boldsymbol{\mathrm{S}}\:=\:\mid\frac{\mathrm{a}}{\mathrm{b}-\mathrm{c}}\mid\:+\:\mid\frac{\mathrm{b}}{\mathrm{c}-\mathrm{a}}\mid\:+\:\mid\frac{\mathrm{c}}{\mathrm{a}-\mathrm{b}}\mid \\ $$

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