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: 81

Answer

$$\frac{5b^2+4ba}{2\left(a+b\right)}$$

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: $$ \frac{\left(8a^3+b^3\right)}{2a^2+3ab+b^2}\times \frac{4b^2+4ab+b^2}{\left(8a^2-4ab+2b^2\right)}\\ \frac{\left(4a^2-2ab+b^2\right)b\left(5b+4a\right)}{\left(a+b\right)\times \:2\left(4a^2-2ab+b^2\right)}\\ \frac{5b^2+4ba}{2\left(a+b\right)}$$
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