Algebra · Algebraic manipulation · Rational expressions · Constraints
Problem 1, 2005
The real numbers \(x\), \(y\), \(z\) satisfy \(xyz = 1\). Compute the value of
\[ \frac{x+1}{xy+x+1} + \frac{y+1}{yz+y+1} + \frac{z+1}{zx+z+1}. \]
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2005, 1. letnik, category A, problem 1. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source