Answer
$\dfrac{2-x}{10-x}$
Work Step by Step
Factoring the given expression, $
\dfrac{1}{10-x}+\dfrac{x-1}{x-10}
,$ results to
\begin{array}{l}\require{cancel}
\dfrac{1}{10-x}+\dfrac{x-1}{-(10-x)}
\\\\=
\dfrac{1}{10-x}-\dfrac{x-1}{10-x}
.\end{array}
Subtracting the numerators and copying the common denominator, the expression above, $
\dfrac{1}{10-x}-\dfrac{x-1}{10-x}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{1-(x-1)}{10-x}
\\\\=
\dfrac{1-x+1}{10-x}
\\\\=
\dfrac{-x+2}{10-x}
\\\\=
\dfrac{2-x}{10-x}
.\end{array}
