Algebra · Rational expressions · Homogeneous equations · Case analysis · Domain conditions
The real numbers \(a\) and \(b\) satisfy
\[ \frac{3a}{a+b} + \frac{2b}{a+2b} = 1 . \]
Determine every value that the expression \(\dfrac{2a-3b}{2a+b}\) can take.
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), odbirno (qualifying) round 2019, 1. letnik, category A, problem 2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source