Answer
$\dfrac{30-x}{6(x-7)}$
Work Step by Step
The factored form of the given equation, $
\dfrac{5}{x-7}-\dfrac{2x}{3x-21}+\dfrac{x}{2x-14}
,$ is
\begin{array}{l}\require{cancel}
\dfrac{5}{x-7}-\dfrac{2x}{3(x-7)}+\dfrac{x}{2(x-7)}
.\end{array}
Using the $LCD=
6(x-7)
,$ then the given equation simplifies to
\begin{array}{l}\require{cancel}
\dfrac{6(5)-2(2x)+3(x)}{6(x-7)}
\\\\
\dfrac{30-4x+3x}{6(x-7)}
\\\\
\dfrac{30-x}{6(x-7)}
.\end{array}
