If ` (x)/( y) = (3)/( 4)` , then value of `(6)/(7) + (y - x)/( y + x)` is

Options

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

Answer

To solve the problem step by step, we start with the given equation and work towards finding the required value.

**Step 1: Understand the given ratio.**
We are given that \( \frac{x}{y} = \frac{3}{4} \). This means that \( x \) and \( y \) are in the ratio of 3 to 4.

**Step 2: Express \( x \) and \( y \) in terms of a common variable.**
Let’s introduce a variable \( k \) such that:
- \( x = 3k \)
- \( y = 4k \)

**Step 3: Substitute \( x \) and \( y \) into the expression.**
We need to find the value of:
\[ \frac{6}{7} + \frac{y - x}{y + x} \]
Substituting \( x \) and \( y \):
\[ \frac{6}{7} + \frac{4k - 3k}{4k + 3k} \]

**Step 4: Simplify the expression.**
Now simplify the fraction:
\[ \frac{4k - 3k}{4k + 3k} = \frac{k}{7k} = \frac{1}{7} \]

**Step 5: Combine the two fractions.**
Now we have:
\[ \frac{6}{7} + \frac{1}{7} \]
Since the denominators are the same, we can add the numerators:
\[ \frac{6 + 1}{7} = \frac{7}{7} = 1 \]

**Final Answer:**
The value of \( \frac{6}{7} + \frac{y - x}{y + x} \) is \( 1 \).

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