If `(x)/(y) = (4)/(5),` then the value of `((4)/(7) + (2y -x )/(2y +x)) ` is :

Options

A. A)`3/7`
B. B)`1 (1)/(7)`
C. C)1
D. D)2

Answer

To solve the problem, we start with the given equation:

\[ \frac{x}{y} = \frac{4}{5} \]

From this, we can express \(x\) in terms of \(y\):

\[ x = \frac{4}{5}y \]

Next, we need to evaluate the expression:

\[ \frac{4}{7} + \frac{2y - x}{2y + x} \]

Substituting \(x = \frac{4}{5}y\) into the expression:

1. **Calculate \(2y - x\)**:
\[ 2y - x = 2y - \frac{4}{5}y = \frac{10}{5}y - \frac{4}{5}y = \frac{6}{5}y \]

2. **Calculate \(2y + x\)**:
\[ 2y + x = 2y + \frac{4}{5}y = \frac{10}{5}y + \frac{4}{5}y = \frac{14}{5}y \]

Now we can substitute these results back into the expression:

\[ \frac{2y - x}{2y + x} = \frac{\frac{6}{5}y}{\frac{14}{5}y} \]

The \(y\) cancels out:

\[ \frac{6}{14} = \frac{3}{7} \]

Now we can substitute this back into the original expression:

\[ \frac{4}{7} + \frac{3}{7} = \frac{4 + 3}{7} = \frac{7}{7} = 1 \]

Thus, the value of the expression is:

\[ \boxed{1} \]