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: 72



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: $$ \frac{z^2-2z+1}{\left(z^2-1\right)\left(4z^2-z-3\right)}\\ \frac{\left(z-1\right)^2}{\left(z-1\right)\left(4z+3\right)\left(z^2-1\right)}\\ \frac{1}{\left(z+1\right)\left(4z+3\right)}$$
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