Given that a * b = \(\frac{a + b}{\text{ab}}\) + (a - b). Find the value of 3 * 2

Answer Details

The problem gives a custom operation: \( a * b = \frac{a + b}{ab} + (a - b) \). You are asked to find the value of 3 * 2.

Let’s break it down step by step:

• Substitute \( a = 3 \) and \( b = 2 \) into the operation:

\[ 3 * 2 = \frac{3 + 2}{3 \times 2} + (3 - 2) \]

• Calculate each part inside the formula:
• \( 3 + 2 = 5 \)
• \( 3 \times 2 = 6 \)
• \( 3 - 2 = 1 \)

\[ 3 * 2 = \frac{5}{6} + 1 \]

• Add the two parts together:

\[ \frac{5}{6} + 1 = \frac{5}{6} + \frac{6}{6} = \frac{11}{6} \]

The custom operation evaluates to \( \frac{11}{6} \). This is obtained by carefully following and substituting values as per the operation’s rule: first forming the fraction from the sum and product, then adding the difference.

Underlying concept: Whenever you’re dealing with a custom operation, always substitute the values EXACTLY as shown in the operation’s formula, and then follow the correct order of operations for arithmetic (first do what's inside parentheses, then multiplication/division, then addition/subtraction).

The value of 3 * 2 is \( \frac{11}{6} \).