ABC26GN0968 · Simplification

$$\begin{aligned} & \frac{x}{2 y}=\frac{6}{7} \Rightarrow \frac{x}{y}=\left(2 \times \frac{6}{7}\right)=\frac{12}{7} . \\ & \therefore \quad \frac{x-y}{x+y}+\frac{14}{19}=\frac{\frac{x}{y}-1}{\frac{x}{y}+1}+\frac{14}{19}=\frac{\frac{12}{7}-1}{\frac{12}{7}+1}+\frac{14}{19}=\frac{(5 / 7)}{(19 / 7)}+\frac{14}{19} \\ & \quad=\left(\frac{5}{7} \times \frac{7}{19}\right)+\frac{14}{19}=\frac{5}{19}+\frac{14}{19}=\frac{19}{19}=1 . \end{aligned}$$