Question

Daca a/b=3/5 calculeaza valoarea raportului 3a+5b/5a+3b


va rog dau coroana​

Answer 1

Răspuns:

17/15

Explicație pas cu pas:

$\displaystyle \frac{a}{b} =\frac{3}{5} \rightarrow a=\frac{3b}{5} \\\\\frac{3a+5b}{5a+3b} =\frac{3\times \frac{3b}{5} +5b}{5\times \frac{3b}{5} +3b} =\frac{\frac{9b}{5} +5b}{\frac{15b}{5} +3b}$

$\displaystyle =\frac{\frac{9b}{5}+\frac{25b}{5} }{\frac{15b}{5}+\frac{15b}{5} } =\frac{\frac{34b}{5} }{\frac{30b}{5} } =\frac{34b}{5} :\frac{30b}{5} =\frac{34b}{\not5} \times \frac{\not5}{30b} =\frac{34\not b}{30\not b} =\frac{34}{30}=\frac{17}{15}$