If a = 2 and b = 3, what is the value of 1/a - 1/b + 1/ab?

To find the value of the expression ( \frac{1}{a} - \frac{1}{b} + \frac{1}{ab} ) given that ( a = 2 ) and ( b = 3 ), we can start by substituting the values of ( a ) and ( b ) into the expression.

1. Calculate ( \frac{1}{a} ):

[

\frac{1}{2}

]

2. Calculate ( \frac{1}{b} ):

[

\frac{1}{3}

]

3. Calculate ( ab ):

[

ab = 2 \cdot 3 = 6

]

Thus, ( \frac{1}{ab} ) is:

[

\frac{1}{6}

]

Now substitute these calculated values back into the expression:

[

\frac{1}{2} - \frac{1}{3} + \frac{1}{6}

]

To combine these fractions, we first need a common denominator. The least common multiple of 2, 3, and 6 is 6. We