Answer
$\dfrac{x}{x^2-1}$
Work Step by Step
The given expression, $
\dfrac{1}{x-x^{-1}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{1}{x-\dfrac{1}{x^1}}
\\\\=
\dfrac{1}{\dfrac{x^2-1}{x}}
\\\\=
\dfrac{x}{x^2-1}
.\end{array}
Intermediate Algebra (6th Edition)
by Martin-Gay, Elayn
Published by
Pearson
ISBN 10:
0321785045
ISBN 13:
978-0-32178-504-6
Chapter 6 - Section 6.3 - Simplifying Complex Fractions - Exercise Set - Page 361: 39
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