Solve 3-(12a-(a:14/a+12)): Complex Algebraic Expression Simplification

To solve this problem, follow these steps:

Start by simplifying the innermost operations and move outward:

• Step 1: Simplify the division inside the parentheses:
  $a : \frac{14}{a} = \frac{a \cdot a}{14} = \frac{a^2}{14}$
• Step 2: Substitute this back into the expression:
  $12a - \left( \frac{a^2}{14} + 12 \right)$
• Step 3: Simplify inside the parenthesis:
  $12a - \left( \frac{a^2}{14} + 12 \right) = 12a - \frac{a^2}{14} - 12$
• Step 4: Distribute the negative sign across the expression within parentheses:
  $3 - (12a - \frac{a^2}{14} - 12) = 3 - 12a + \frac{a^2}{14} + 12$
• Step 5: Combine the constant terms:
  $3 + 12 - 12a + \frac{a^2}{14} = 15 - 12a + \frac{a^2}{14}$

Thus, the expression simplifies to $15 - 12a + \frac{a^2}{14}$.