The value of `(4-3 div 2 xx (4-2)-3 + 4 xx 3 div 2 + 4)/(4 + 3 div 4 xx (2-4) xx 4 + 3 div 4 of 3)` is .............

Options

A. `-32`
B. 32
C. `(-32)/(7)`
D. `(32)/(7)`

Answer

To solve the expression \((4 - 3 \div 2 \times (4 - 2) - 3 + 4 \times 3 \div 2 + 4) / (4 + 3 \div 4 \times (2 - 4) \times 4 + 3 \div 4 \times 3)\), we will follow the BODMAS/BIDMAS rule (Brackets, Orders, Division and Multiplication, Addition and Subtraction).

### Step-by-Step Solution:

1. **Evaluate the brackets**:
- In the numerator: \(4 - 2 = 2\)
- In the denominator: \(2 - 4 = -2\)

The expression now looks like:
\[ \frac{(4 - 3 \div 2 \times 2 - 3 + 4 \times 3 \div 2 + 4)}{(4 + 3 \div 4 \times -2 \times 4 + 3 \div 4 \times 3)} \]

2. **Perform the divisions and multiplications from left to right**:
- In the numerator:
- \(3 \div 2 = 1.5\)
- \(4 \times 3 = 12\)
- \(12 \div 2 = 6\)

The numerator simplifies to:
\[ 4 - 1.5 \times 2 - 3 + 6 + 4 \]

- In the denominator:
- \(3 \div 4 = 0.75\)
- \(0.75 \times -2 = -1.5\)
- \(-1.5 \times 4 = -6\)
- \(3 \div 4 \times 3 = 0.75 \times 3 = 2.25\)

The denominator simplifies to:
\[ 4 - 6 + 2.25 \]

3. **Substituting back into the expression**:
- The numerator becomes:
\[ 4 - 3 + 6 + 4 - 3 = 8.5 \]
- The denominator becomes:
\[ 4 - 6 + 2.25 = 0.25 \]

4. **Final calculation**:
\[ \frac{8.5}{0.25} = 34 \]

### Final Answer:
The value of the expression is \(34\).