[tex] \frac{5x+6y}{6x-5y}= \frac{16}{17}, \frac{y(5 \frac{x}{y} +6)}{y(6 \frac{x}{y} -5)}= \frac{16}{17} \\\frac{5 \frac{x}{y} +6}{6 \frac{x}{y} -5}= \frac{16}{17} \\ 17(5 \frac{x}{y} +6)=16(6 \frac{x}{y} -5) \\ 85 \frac{x}{y} +102=96 \frac{x}{y} -80 \\ 96 \frac{x}{y}-85 \frac{x}{y}=102+80 \\ 11 \frac{x}{y} =182 \\ \frac{x}{y} = \frac{182}{11} [/tex]
