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