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Poblem 4 (2nd jbmo tst)

Source: 2nd TST for JBMO, Moldova

March 31, 2006
quadraticsalgebraalgebra proposed

Problem Statement

Determine all real solutions of the equation: x2x−1+x−1+x−1x2=x−1x2+1x−1+x2x−1.{ \frac{x^{2}}{x-1}+\sqrt{x-1}+\frac{\sqrt{x-1}}{x^{2}}}=\frac{x-1}{x^{2}}+\frac{1}{\sqrt{x-1}}+\frac{x^{2}}{\sqrt{x-1}} .
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