# How do you evaluate #\lim _ { x \rightarrow 2} \frac { \frac { 1} { x } - \frac { 1} { 2} } { x - 2}#?

##### 2 Answers

#### Explanation:

Using L'Hôpital's rule, we can differentiate both numerator and denominator, and the limit in question is equal to the new limit, that is:

#### Explanation:

For those who have not learned L'Hopital's Rule, an alternative method relies upon some clever manipulations. First, combine the fractions in the numerator:

Now, factor out a -1 from the numerator of the combined fraction in the numerator, and then simplify the entire expression: