Answer
$\lim _{x\rightarrow 3 ^{-}}\dfrac {x-3}{\left| x-3\right| }=-1$
Work Step by Step
$x < a\Rightarrow \left| x-a\right| =a-x\Rightarrow \lim _{x\rightarrow 3 ^{-}}\left| x-3\right| =\left( 3-x\right) $
$\lim _{x\rightarrow 3 ^{-}}\dfrac {\left( x-3\right) }{\left| x-3\right| }=\dfrac {x-3}{3-x}=-1$
