9/14 * 17/24 - 5/12

To solve the expression \( \frac{9}{14} \times \frac{17}{24} - \frac{5}{12} \), we follow these steps:

1. Multiply the fractions: \[ \frac{9}{14} \times \frac{17}{24} = \frac{9 \times 17}{14 \times 24} = \frac{153}{336} \]

2. Simplify \( \frac{153}{336} \): We find the greatest common divisor (GCD) of 153 and 336. The factors of 153 are \( 3 \times 51 = 3 \times 3 \times 17 \) and the factors of 336 are \( 2^4 \times 3 \times 7 \). The common factor is \( 3 \): \[ \frac{153 \div 3}{336 \div 3} = \frac{51}{112} \]

3. Convert \( \frac{5}{12} \) to a common denominator with \( \frac{51}{112} \): The least common multiple (LCM) of 112 and 12 is 336. We convert \( \frac{5}{12} \): \[ \frac{5}{12} = \frac{5 \times 28}{12 \times 28} = \frac{140}{336} \]

4. Subtract the two fractions: Now we have: \[ \frac{51}{112} = \frac{153}{336} \quad \text{and} \quad \frac{5}{12} = \frac{140}{336} \] Substituting in gives: \[ \frac{153}{336} - \frac{140}{336} = \frac{153 - 140}{336} = \frac{13}{336} \]

Thus, the final answer is: \[ \frac{13}{336} \]