Evaluate : `(9|3-5|-5|4| + 10)/(-3(5) - 2 xx 4 + 2)`

Options

A. `(9)/(10)`
B. `-(8)/(21)`
C. `-(16)/(19)`
D. `(4)/(7)`

Answer

To evaluate the expression \((9|3-5|-5|4| + 10)/(-3(5) - 2 \times 4 + 2)\), we will follow these steps:

### Step 1: Simplify the absolute values
First, we need to evaluate the absolute values in the expression.
- Calculate \(3 - 5 = -2\), so \(|3 - 5| = 2\).
- Calculate \(|4| = 4\) (since 4 is already positive).

Now we can rewrite the expression:
\[ (9 \cdot 2 - 5 \cdot 4 + 10) \]

### Step 2: Substitute the absolute values into the expression
Substituting the values we calculated, we have:
\[ (9 \cdot 2 - 5 \cdot 4 + 10) = (18 - 20 + 10) \]

### Step 3: Simplify the numerator
Now, simplify the numerator:
\[ 18 - 20 + 10 = 18 - 20 = -2 \quad \text{and} \quad -2 + 10 = 8 \]
So, the numerator is \(8\).

### Step 4: Simplify the denominator
Now, we will simplify the denominator:
\[ -3(5) - 2 \times 4 + 2 \]
Calculating each term:
- \(-3 \cdot 5 = -15\)
- \(-2 \cdot 4 = -8\)

Now substituting these values into the denominator:
\[ -15 - 8 + 2 = -15 - 8 = -23 \quad \text{and} \quad -23 + 2 = -21 \]
So, the denominator is \(-21\).

### Step 5: Combine the results
Now we can combine the results from the numerator and denominator:
\[ \frac{8}{-21} = -\frac{8}{21} \]

### Final Answer
Thus, the final answer is:
\[ -\frac{8}{21} \]

---