Gọi ba phân số đó là \(\frac{a}{x};\frac{b}{y};\frac{c}{z}\). Theo bài ra ta có:
\(a:b:c=3:4:5\Rightarrow a=3m;b=4m;c=5m\)
\(x:y:z=5:1:2\Rightarrow x=5n;y=n;z=2n\)
\(\Rightarrow\frac{a}{x}+\frac{b}{y}+\frac{c}{z}=\frac{3m}{5n}+\frac{4m}{n}+\frac{5m}{2n}=\frac{213}{70}\)
\(\Rightarrow\frac{3}{5}\cdot\frac{m}{n}+4\cdot\frac{m}{n}+\frac{5}{2}\cdot\frac{m}{n}=\frac{213}{70}\)
\(\Rightarrow\left(\frac{3}{5}+4+\frac{5}{2}\right)\cdot\frac{m}{n}=\frac{213}{70}\)
\(\Rightarrow\frac{71}{10}\cdot\frac{m}{n}=\frac{213}{70}\)
\(\Rightarrow\frac{m}{n}=\frac{3}{7}\)\(\Rightarrow\frac{a}{x}=\frac{9}{35};\frac{b}{y}=\frac{12}{7};\frac{c}{z}=\frac{15}{14}\)
học tốt
