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: 65

Answer

$$\frac{a-5}{3\left(a-1\right)}$$

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: $$ \frac{\left(a+2\right)}{a-1}\times \frac{a-5}{\left(3a+6\right)}\\ \frac{\left(a+2\right)\left(a-5\right)}{\left(a-1\right)\left(3a+6\right)}\\ \frac{\left(a+2\right)\left(a-5\right)}{\left(a-1\right)\times \:3\left(a+2\right)}\\ \frac{a-5}{3\left(a-1\right)}$$
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