Correct Answer: $1$

Solution : Given: $\frac{x}{y}=\frac{4}{5}$
Divide $y$ in both numerator and denominator of the fraction, $\frac{2y – x}{2y+x}$, we get,
$\frac{2–\frac{x}{y}}{2+\frac{x}{y}}$
Substitute the value of $\frac{x}{y}=\frac{4}{5}$ in the above equation, we get,
= $\frac{2–\frac{4}{5}}{2+\frac{4}{5}}$
= $\frac{\frac{10–4}{5}}{\frac{10+4}{5}}=\frac{6}{14}=\frac{3}{7}$
The value of the expression $(\frac{4}{7}+\frac{2y–x}{2y+x})$ is given as,
$(\frac{4}{7}+\frac{3}{7})=(\frac{4+3}{7})=\frac{7}{7}=1$
Hence, the correct answer is $1$.