Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 11 - Rational Expressions and Functions - 11-2 Multiplying and Dividing Rational Expressions - Lesson Check: 3

Answer

$(k+1)(3k^2)$

Work Step by Step

The reciprocal of a fraction $\frac{x}{y}$ is $\frac{y}{x}$. Dividing by a fraction is the same as multiplying by that fraction's reciprocal. First, we have to multiply together the numerators and the denominators: $\frac{k^2+k}{5k}\div\frac{1}{15k^2} = \frac{k^2+k}{5k}\cdot\frac{15k^2}{1} = \frac{(k^2+k)(15k^2)}{5k}$ Then, we simplify: $\frac{5k(k+1)(3k^2)}{5k} = \frac{(k+1)(3k^2)}{1} = (k+1)(3k^2)$ We leave this product in factored form
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