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: 68

Answer

$$\frac{\left(a+7\right)\left(a+1\right)}{3a-7}$$

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: $$ \frac{\left(a+7\right)\left(a^2+8a+7\right)}{3a^2+14a-49}\\ \frac{\left(a+7\right)^2\left(a+1\right)}{\left(3a-7\right)\left(a+7\right)}]\\ \frac{\left(a+7\right)\left(a+1\right)}{3a-7}$$
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