Answer
$-1$
Work Step by Step
The given expression, $
\dfrac{3+2x}{10-x}+\dfrac{13+x}{x-10}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{3+2x}{10-x}+\dfrac{13+x}{-(10-x)}
\\\\=
\dfrac{3+2x}{10-x}-\dfrac{13+x}{10-x}
\\\\=
\dfrac{3+2x-(13+x)}{10-x}
\\\\=
\dfrac{3+2x-13-x}{10-x}
\\\\=
\dfrac{-10+x}{10-x}
\\\\=
\dfrac{-(10-x)}{10-x}
\\\\=
\dfrac{-(\cancel{10-x})}{\cancel{10-x}}
\\\\=
-1
.\end{array}
