Algebra · Rational equations · Factorisation · Homogeneous expressions
Real numbers \(a\) and \(b\) satisfy \(|a| \ne |b|\) and \(a \ne 0\), together with
\[ \frac{a-b}{a^{2}+ab} + \frac{a+b}{a^{2}-ab} = \frac{3a-b}{a^{2}-b^{2}} . \]
Determine the value of \(\dfrac{b}{a}\).
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2014, 1. letnik, category A, problem 1. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source