Question

Daca 3x-2y/4x+y =2/3 atunci x/y este

/ = supra

Answer 1

    
$\frac{3x-2y}{4x+y} = \frac{3}{2} \\ \text{Fractia din stanga egalului, o simplificam }\underline{fortat}\; cu \; ( y) \\ \\ \frac{3 \frac{x}{y} -2 \frac{y}{y} }{4 \frac{x}{y} + \frac{y}{y}} = \frac{3}{2} \\ \\ \frac{3 \frac{x}{y} -2 }{4 \frac{x}{y} + 1} = \frac{3}{2} \\ \\ 3 \frac{x}{y} -2= \frac{3}{2} \cdot (4 \frac{x}{y} + 1)$

$3\cdot \frac{x}{y} -2= \frac{3 \cdot 4}{2} \cdot \frac{x}{y} +- \frac{3}{2} \\ \\ 3\cdot \frac{x}{y} -2= 6\cdot \frac{x}{y} + \frac{3}{2} \\ \\ 6\cdot \frac{x}{y}-3\cdot \frac{x}{y}=-2-\frac{3}{2} \\ \\ 3\cdot \frac{x}{y}=- \frac{4}{2} -\frac{3}{2} \\ \\ 3\cdot \frac{x}{y}=- \frac{7}{2} \\ \\ \frac{x}{y}= \frac{- \frac{7}{2} }{3} = - \frac{7}{2\; \cdot \;3} =\boxed{- \frac{7}{6}}$