Explicație pas cu pas:
[tex]5x = 3y = > \frac{x}{y} = \frac{3}{5} [/tex]
[tex]5x = 3y = k = > \\ 5x = k = > x = \frac{k}{5} \\ 3y = k = > y = \frac{k}{3} [/tex]
[tex] \frac{5x - 2y}{6x - 3y} = \frac{5 \times \frac{k}{5} - 2 \times \frac{k}{3} }{6 \times \frac{k}{5} - 3 \times \frac{k}{3} } \\ = \frac{k(1 - \frac{2}{3}) }{k( \frac{6}{5} - 1) } = \frac{ \frac{3 - 2}{3} }{ \frac{6 - 5}{5} } = \frac{ \frac{1}{3} }{ \frac{1}{5} } = \frac{5}{3} [/tex]
sau:
știm că 5x = 3y
și:
[tex] \frac{x}{y} = \frac{3}{5} => \frac{y}{x} = \frac{5}{3} [/tex]
=>
[tex] \frac{5x - 2y}{6x - 3y} = \frac{3y - 2y}{6x - 5x} = \frac{y}{x} = \frac{5}{3}[/tex]
