Răspuns
[tex] \dfrac{15}{22} [/tex]
Explicație pas cu pas:
[tex](x,y)~invers~proportional~(5,8)\Rightarrow \dfrac{x}{\frac{1}{5}}=\dfrac{y}{\frac{1}{8}}=k\Rightarrow x=\dfrac{k}{5},y=\dfrac{k}{8}\\\dfrac{5x-2y}{3x+4y}=\dfrac{5\cdot \frac{k}{5}-2\cdot\frac{k}{8}}{3\cdot \frac{k}{5}+4\cdot \frac{k}{8}}= \dfrac{k-\frac{k}{4}}{ \frac{3k}{5}+\frac{k}{2}}=\dfrac{\frac{4k-k}{4}}{\frac{6k+5k}{10}}=\dfrac{\frac{3k}{4}}{\frac{11k}{10}}=\dfrac{3}{4}\cdot \dfrac{10}{11}=\bold{\dfrac{15}{22}}[/tex]
