Algebra · Rational expressions · Factorisation · Constraint equation · Case analysis
Let \(a\) and \(b\) be real numbers satisfying
\[ \frac{a^2}{1+a^2} + \frac{b^2}{1+b^2} = 1 . \]
Determine all possible values of the expression
\[ (a+b)\left( \frac{a}{1+a^2} + \frac{b}{1+b^2} \right) . \]
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), regijsko (regional) round 2015, 1. letnik, category A, problem B3. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source