# How do you find the limit of ((1/(x+3))-(1/3))/x as x approaches 0?

Aug 7, 2018

$\frac{\left(\frac{1}{x + 3}\right) - \left(\frac{1}{3}\right)}{x} {|}_{x \to 0}$

$= \frac{\frac{3 - \left(x + 3\right)}{3 \left(x + 3\right)}}{x} {|}_{x \to 0}$

$= - \frac{\frac{x}{3 \left(x + 3\right)}}{x} {|}_{x \to 0}$

$= - \frac{x}{3 x \left(x + 3\right)} {|}_{x \to 0}$

$= - \frac{1}{3 \left(x + 3\right)} {|}_{x \to 0}$

$= - \frac{1}{9}$