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