Question

`( (1)/( x) - (1)/(12) )/(x - 12)`

how do i solve when looking for the limit as x approches 12?​

Answer 1

`\lim_(x \to 12) ((1)/(x)-(1)/(12) )/(x-12) =(-1)/(144)`

Explanation:

Step 1: Define

`\lim_(x \to 12) ((1)/(x)-(1)/(12) )/(x-12)`

Step 2: Solve

1. Numerator; Common denominator:
   `\lim_(x \to 12) ((12)/(12x)-(x)/(12x) )/(x-12)`
2. Numerator; Combine like terms:
   `\lim_(x \to 12) ((12-x)/(12x) )/(x-12)`
3. Rewrite entire fraction:
   `\lim_(x \to 12) (12-x)/(12x) / x-12`
4. Rewrite operation:
   `\lim_(x \to 12) (12-x)/(12x) \cdot (1)/(x-12)`
5. Multiply:
   `\lim_(x \to 12) (12-x)/(12x(x-12))`
6. Factor numerator:
   `\lim_(x \to 12) (-(x - 12))/(12x(x-12))`
7. Simplify:
   `\lim_(x \to 12) (-1)/(12x)`
8. Evaluate limit:
   `(-1)/(12(12)) =(-1)/(144)`