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: 80


$$ \frac{4y^2+6y+9}{8y^2+10y-3}$$

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: $$ \frac{\left(8y^3-27\right)}{64y^3-1}\times \frac{16y^2+4y+1}{\left(4y^2-9\right)}\\ \frac{\left(2y-3\right)\left(4y^2+6y+9\right)\left(16y^2+4y+1\right)}{\left(4y-1\right)\left(16y^2+4y+1\right)\left(2y+3\right)\left(2y-3\right)}\\ \frac{4y^2+6y+9}{\left(4y-1\right)\left(2y+3\right)}\\ \frac{4y^2+6y+9}{8y^2+10y-3}$$
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