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