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Stiind ca [tex] \frac{2x}{9y} [/tex]=0,2(7),calculati valoarea raportului [tex] \frac{8x+5y}{9x-5y}[/tex]

Răspuns :

Din egalitatea data obtinem
[tex]\dfrac xy=\dfrac{25}{90}\cdot\dfrac92\Rightarrow \dfrac xy=\dfrac54\Rightarrow x=\dfrac{5y}{4}[/tex] si inlocuim in fractia ce trebuie calculata
[tex]...=\dfrac{8\cdot\dfrac{5y}{4}+5y}{9\cdot\dfrac{5y}{4}-5y}=\dfrac{40y+20y}{45y-20y}=\dfrac{60}{25}=\dfrac{12}{5} [/tex]