If `b/a = 3/5` then `(3a-5b)/(3a+5b)` = ?

Options

A. (a) 0
B. (b) 1
C. (c) 11
D. (d) 35

Answer

To solve the problem, we start with the given ratio \( \frac{b}{a} = \frac{3}{5} \). We need to find the value of \( \frac{3a - 5b}{3a + 5b} \).

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

### Step 2: Substitute \( b \) in the expression
Now we substitute \( b \) in the expression \( \frac{3a - 5b}{3a + 5b} \):
\[ \frac{3a - 5\left(\frac{3}{5}a\right)}{3a + 5\left(\frac{3}{5}a\right)} \]

### Step 3: Simplify the numerator
Calculating the numerator:
\[ 3a - 5\left(\frac{3}{5}a\right) = 3a - 3a = 0 \]

### Step 4: Simplify the denominator
Calculating the denominator:
\[ 3a + 5\left(\frac{3}{5}a\right) = 3a + 3a = 6a \]

### Step 5: Combine the results
Now we can combine the simplified numerator and denominator:
\[ \frac{0}{6a} = 0 \]

### Final Answer
Thus, the value of \( \frac{3a - 5b}{3a + 5b} \) is:
\[ \boxed{0} \]