Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 6 - Rational Expressions and Equations - 6.2 Multiplication and Division - 6.2 Exercise Set - Page 385: 71



Work Step by Step

Recall, one never divides by a fraction. Rather, if we want to divide by a fraction, we multiply by the reciprocal of the fraction. Recall, the reciprocal of a fraction is that fraction with the numerator and the denominator switched. Thus, we find: $$ \frac{c^2+10c+21}{\left(c^2-2c-15\right)\left(5c^2+32c-21\right)}\\ \frac{\left(c+3\right)\left(c+7\right)}{\left(c+3\right)\left(c-5\right)\left(5c-3\right)\left(c+7\right)}\\ \frac{1}{\left(c-5\right)\left(5c-3\right)}$$
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