[tex]x=\frac{4}{9}y \Rightarrow \frac{3x+2y}{5x+y}=\frac{3\cdot\frac{4}{9}y+2y}{5\cdot\frac{4}{9}y+y}=\\
\frac{y(\frac{4}{3}+2)}{y(\frac{20}{9}+1)}=\frac{\frac{4}{3}+2}{\frac{20}{9}+1}=\frac{10}{3}\cdot\frac{9}{29}=\frac{30}{29}[/tex]
[tex]x=\frac{3}{5}y \Rightarrow \frac{4x+6y}{x+y}=\frac{4\cdot\frac{3}{5}y+6y}{\frac{3}{5}y+y}=\\\frac{y(\frac{12}{5}+6)}{y(\frac{3}{5}+1)}=\frac{\frac{12}{5}+6}{\frac{3}{5}+1}=\frac{42}{5}\cdot\frac{5}{8}=\frac{42}{8}=\frac{21}{4}[/tex]
