If $\frac{X}{2Y}=\frac{6}{7}$, find the value of $\frac{X-Y}{X+Y}+\frac{14}{19}$.

Given:
$$\frac{X}{2Y}=\frac{6}{7}⟹\frac{X}{Y}=\frac{12}{7}$$

Let $X=12k$ and $Y=7k$. Substitute these values into the given expression:

$$\frac{X-Y}{X+Y}=\frac{12k-7k}{12k+7k}=\frac{5k}{19k}=\frac{5}{19}$$

Now add $\frac{14}{19}$:

$$\frac{5}{19}+\frac{14}{19}=\frac{5+14}{19}=\frac{19}{19}=1$$