`10-{17-12 div (59 + 9 xx 2 -17)}` is equal to :

Options

A. `-5`
B. `7`
C. 5
D. `-(34)/(5)`

Answer

To solve the expression \( 10 - \{ 17 - \frac{12}{(59 + 9 \times 2 - 17)} \} \), we will follow the order of operations (brackets, orders, division and multiplication, addition and subtraction).

### Step-by-Step Solution:

1. **Evaluate the innermost bracket**:
\[ 59 + 9 \times 2 - 17 \]
First, calculate \( 9 \times 2 \):
\[ 9 \times 2 = 18 \]
Now substitute back into the expression:
\[ 59 + 18 - 17 \]
Next, perform the addition and subtraction:
\[ 59 + 18 = 77 \]
\[ 77 - 17 = 60 \]
So, the innermost bracket evaluates to \( 60 \).

2. **Substitute back into the expression**:
Now we have:
\[ 10 - \{ 17 - \frac{12}{60} \} \]

3. **Simplify the fraction**:
Calculate \( \frac{12}{60} \):
\[ \frac{12}{60} = \frac{1}{5} \]
Substitute this back into the expression:
\[ 10 - \{ 17 - \frac{1}{5} \} \]

4. **Evaluate the expression inside the brackets**:
Now calculate \( 17 - \frac{1}{5} \):
To subtract, convert \( 17 \) into a fraction:
\[ 17 = \frac{85}{5} \]
Now perform the subtraction:
\[ \frac{85}{5} - \frac{1}{5} = \frac{84}{5} \]

5. **Substitute back into the expression**:
Now we have:
\[ 10 - \frac{84}{5} \]

6. **Convert \( 10 \) into a fraction**:
Convert \( 10 \) into a fraction with a denominator of \( 5 \):
\[ 10 = \frac{50}{5} \]
Now perform the subtraction:
\[ \frac{50}{5} - \frac{84}{5} = \frac{50 - 84}{5} = \frac{-34}{5} \]

### Final Answer:
Thus, the expression \( 10 - \{ 17 - \frac{12}{(59 + 9 \times 2 - 17)} \} \) is equal to:
\[ \frac{-34}{5} \]