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solve real equation

Source: Argentina IMO TST 2007 problem 4

August 27, 2009
algebra unsolvedalgebra

Problem Statement

Find all real values of x>1 x>1 which satisfy: \frac{x^2}{x\minus{}1} \plus{} \sqrt{x\minus{}1} \plus{}\frac{\sqrt{x\minus{}1}}{x^2} \equal{} \frac{x\minus{}1}{x^2} \plus{} \frac{1}{\sqrt{x\minus{}1}} \plus{} \frac{x^2}{\sqrt{x\minus{}1}}