If `x/y=5/3`, then `(x+y)/(x-y)` is equal to :

Options

A. A)4
B. B)2
C. C)-2
D. D)-4

Answer

To solve the problem, we start with the given ratio \( \frac{x}{y} = \frac{5}{3} \).

### Step 1: Express \( x \) in terms of \( y \)
From the ratio, we can express \( x \) as:
\[ x = \frac{5}{3}y \]

**Hint:** Use the given ratio to express one variable in terms of the other.

### Step 2: Substitute \( x \) into the expression \( \frac{x+y}{x-y} \)
Now we need to find \( \frac{x+y}{x-y} \). We substitute \( x \) from Step 1:
\[ \frac{x+y}{x-y} = \frac{\frac{5}{3}y + y}{\frac{5}{3}y - y} \]

**Hint:** Substitute the expression for \( x \) into the fraction.

### Step 3: Simplify the numerator and denominator
First, simplify the numerator:
\[ \frac{5}{3}y + y = \frac{5}{3}y + \frac{3}{3}y = \frac{5y + 3y}{3} = \frac{8y}{3} \]

Now simplify the denominator:
\[ \frac{5}{3}y - y = \frac{5}{3}y - \frac{3}{3}y = \frac{5y - 3y}{3} = \frac{2y}{3} \]

**Hint:** Combine like terms in both the numerator and denominator.

### Step 4: Write the expression with simplified numerator and denominator
Now we can write the expression as:
\[ \frac{x+y}{x-y} = \frac{\frac{8y}{3}}{\frac{2y}{3}} \]

**Hint:** You can simplify the fraction by dividing the numerator by the denominator.

### Step 5: Simplify the fraction
When we divide the two fractions, we multiply by the reciprocal of the denominator:
\[ \frac{\frac{8y}{3}}{\frac{2y}{3}} = \frac{8y}{3} \times \frac{3}{2y} = \frac{8 \cancel{y}}{2 \cancel{y}} = \frac{8}{2} = 4 \]

**Hint:** Cancel out common factors in the numerator and denominator.

### Final Answer
Thus, the value of \( \frac{x+y}{x-y} \) is:
\[ \boxed{4} \]