[tex] \displaystyle\\
\frac{3a-2b}{5a+b} =\frac{1}{3} \\\\
\text{Fractia din stanga o simplificam fortat cu b.}\\\\
\frac{3\cdot \dfrac{a}{b}-2\cdot\dfrac{b}{b}}{5\cdot \dfrac{a}{b}+\dfrac{b}{b}} =\frac{1}{3} \\\\\\
\frac{3\cdot \dfrac{a}{b}-2}{5\cdot \dfrac{a}{b}+1} =\frac{1}{3} [/tex]
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[tex] \displaystyle\\
\text{Produsul mezilor egal cu produsul extremilor.}\\\\
3\Big( 3\cdot \dfrac{a}{b}-2 \Big) = 1\Big( 5\cdot \dfrac{a}{b}+1\Big)\\\\
9\cdot \frac{a}{b}-6 = 5\cdot \frac{a}{b}+1\\\\
9\cdot \frac{a}{b}-5\cdot \frac{a}{b} = 1+6\\\\
4\cdot \frac{a}{b} = 7\\\\
\boxed{\bf \frac{a}{b} = \frac{7}{4}} [/tex]