College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.5 - Rational Expressions - R.5 Exercises - Page 48: 75



Work Step by Step

The given expression, $ \dfrac{\dfrac{1}{x+h}-\dfrac{1}{x}}{h} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\dfrac{x(1)-(x+h)(1)}{x(x+h)}}{h} \\\\= \dfrac{x(1)-(x+h)(1)}{x(x+h)}\div h \\\\= \dfrac{x(1)-(x+h)(1)}{x(x+h)}\cdot\dfrac{1}{h} \\\\= \dfrac{x(1)-(x+h)(1)}{xh(x+h)} \\\\= \dfrac{x-x-h}{xh(x+h)} \\\\= \dfrac{-h}{xh(x+h)} \\\\= \dfrac{-\cancel{h}}{x\cancel{h}(x+h)} \\\\= -\dfrac{1}{x(x+h)} .\end{array}
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