[tex]\displaystyle \frac{x}{y} = \frac{4}{9} =>x= \frac{4y}{9} \\
\frac{3x+2y}{5x+y} = \frac{3\cdot \frac{4y}{9}+2y}{5 \cdot \frac{4y}{9}+y } = \frac{y( \frac{12}{9}+2) }{y(\frac{20}{9}+1)}= \frac{\frac{12}{9}+2}{\frac{20}{9}+1} = \frac{\frac{30}{9}}{\frac{29}{9}} \\
=\frac{30}{9}:\frac{29}{9}}=\frac{30}{9} \cdot \frac{9}{29}}= \frac{30}{29} [/tex]
