Answer
$\dfrac{3}{2(x-2)}$
Work Step by Step
Factoring the given expression, $
\dfrac{1}{x-2}-\dfrac{1}{4-2x}
,$ results to
\begin{array}{l}\require{cancel}
\dfrac{1}{x-2}-\dfrac{1}{2(2-x)}
\\\\=
\dfrac{1}{x-2}-\dfrac{1}{-2(x-2)}
\\\\=
\dfrac{1}{x-2}+\dfrac{1}{2(x-2)}
.\end{array}
Using the $LCD=
2(x-2)
$, the expression above simplifies to
\begin{array}{l}\require{cancel}
\dfrac{2+1}{2(x-2)}
\\\\=
\dfrac{3}{2(x-2)}
.\end{array}
