Simplify \( \frac{67-2(10 \div 2 \cdot 5)-3^{2}}{|2-5|+-5} \)

1. **Simplify the numerator:** The numerator is \[ 67 - 2\left(10 \div 2 \cdot 5\right) - 3^2. \] - First, evaluate the exponent: \[ 3^2 = 9. \] - Next, simplify the expression inside the parentheses. Since division and multiplication have equal precedence, evaluate from left to right: \[ 10 \div 2 = 5,\quad 5 \cdot 5 = 25. \] - Substitute back into the numerator: \[ 67 - 2 \cdot 25 - 9. \] - Now perform the multiplication: \[ 2 \cdot 25 = 50. \] - Finally, subtract: \[ 67 - 50 = 17,\quad 17 - 9 = 8. \] So, the numerator simplifies to \(8\). 2. **Simplify the denominator:** The denominator is \[ |2 - 5| + -5. \] - Calculate the expression inside the absolute value: \[ 2 - 5 = -3. \] - Take the absolute value: \[ |{-3}| = 3. \] - Now add \(-5\): \[ 3 + (-5) = -2. \] So, the denominator simplifies to \(-2\). 3. **Form the simplified fraction:** \[ \frac{8}{-2} = -4. \] Thus, the simplified expression is \(-4\).