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 386: 97



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: $$ \frac{3a^2-5ab-12b^2}{\left(3ab+4b^2\right)\left(3b^2-ab\right)^2}\\ \frac{\left(3a+4b\right)\left(a-3b\right)}{b^3\left(3b-a\right)^2\left(3a+4b\right)}\\ \frac{1}{b^3\left(a-3b\right)}$$
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