[tex]\it \dfrac{x+y}{2x+3y} = \dfrac{8}{19} \stackrel{derivare}{\Longrightarrow} \dfrac{x+y}{2x+3y-x-y} =\dfrac{8}{19-8} \Rightarrow \dfrac{x+y}{x+2y} = \dfrac{8}{11} \Rightarrow
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\stackrel{derivare}{\Longrightarrow} \dfrac{x+y}{x+2y-x-y} =\dfrac{8}{11-8} \Rightarrow \dfrac{x+y}{y} = \dfrac{8}{3} \Rightarrow \dfrac{x}{y} +\dfrac{y}{y} = \dfrac{8}{3}\Rightarrow
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\Rightarrow \dfrac{x}{y} +1 = \dfrac{8}{3} \Rightarrow \dfrac{x}{y} = \dfrac{8}{3}-1 \Rightarrow \dfrac{x}{y} = \dfrac{5}{3}[/tex]
