# How do you find the limit of (1/x-1/2)/(x-2) as x->2?

Nov 22, 2016

${\lim}_{x \to 2} \frac{\frac{1}{x} - \frac{1}{2}}{x - 2}$

Simplify the equation:

$= {\lim}_{x \to 2} \frac{\frac{2 - x}{2 x}}{x - 2}$

$= {\lim}_{x \to 2} \frac{2 - x}{\left(2 x\right) \left(x - 2\right)}$

Manipulate the equation to simplify further:

$= {\lim}_{x \to 2} \frac{- \left(x - 2\right)}{\left(2 x\right) \left(x - 2\right)}$

Cancel and solve:

$= {\lim}_{x \to 2} \frac{- 1}{\left(2 x\right)} = - \frac{1}{4}$