Question

Stiind ca 3a minus 2b supra 5a plus b egal cu 1 supra 3 atunci a supra b este

Answer 1

$\displaystyle\\ \frac{3a-2b}{5a+b} =\frac{1}{3} \\\\ \text{Fractia din stanga o simplificam fortat cu b.}\\\\ \frac{3\cdot \dfrac{a}{b}-2\cdot\dfrac{b}{b}}{5\cdot \dfrac{a}{b}+\dfrac{b}{b}} =\frac{1}{3} \\\\\\ \frac{3\cdot \dfrac{a}{b}-2}{5\cdot \dfrac{a}{b}+1} =\frac{1}{3}$

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$\displaystyle\\ \text{Produsul mezilor egal cu produsul extremilor.}\\\\ 3\Big( 3\cdot \dfrac{a}{b}-2 \Big) = 1\Big( 5\cdot \dfrac{a}{b}+1\Big)\\\\ 9\cdot \frac{a}{b}-6 = 5\cdot \frac{a}{b}+1\\\\ 9\cdot \frac{a}{b}-5\cdot \frac{a}{b} = 1+6\\\\ 4\cdot \frac{a}{b} = 7\\\\ \boxed{\bf \frac{a}{b} = \frac{7}{4}}$