Answer
$-x^2+x$
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}{x-1}}
\\\\=
\dfrac{x}{1-\dfrac{x}{x-1}}
\\\\=
\dfrac{x}{\dfrac{x-1-x}{x-1}}
\\\\=
\dfrac{x}{\dfrac{-1}{x-1}}
\\\\=
x\div\dfrac{-1}{x-1}
\\\\=
x\cdot\dfrac{x-1}{-1}
\\\\=
\dfrac{x^2-x}{-1}
\\\\=
-x^2+x
.\end{array}
