If `a^(**)b=a+b+(a)/(b)`, then the value of `12^(**)4` is

Options

A. 20
B. 21
C. 48
D. 19

Answer

To solve the problem, we need to evaluate the expression \( 12^{(**)}4 \) using the given operation defined as \( a^{(**)}b = a + b + \frac{a}{b} \).

### Step-by-Step Solution:

1. **Identify the values of \( a \) and \( b \)**:
- Here, \( a = 12 \) and \( b = 4 \).

2. **Apply the operation definition**:
- According to the definition, we have:
\[ 12^{(**)}4 = 12 + 4 + \frac{12}{4} \]

3. **Calculate \( 12 + 4 \)**:
- Adding these two numbers gives:
\[ 12 + 4 = 16 \]

4. **Calculate \( \frac{12}{4} \)**:
- Dividing \( 12 \) by \( 4 \) results in:
\[ \frac{12}{4} = 3 \]

5. **Combine the results**:
- Now, we add the results from steps 3 and 4:
\[ 16 + 3 = 19 \]

6. **Final Result**:
- Therefore, the value of \( 12^{(**)}4 \) is:
\[ \boxed{19} \]