Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter R - Review of Basic Concepts - R.3 Polynomials - R.3 Exercises: 98

Answer

$$2r^{2}+3rs-5s^{2}$$

Work Step by Step

Initial equation: $$\frac{-8r^{3}s-12r^{2}s^{2}+20rs^{3}}{-4rs}$$ Begin by factoring both the numerator and denominator. In this case, only the numerator factors, and is done so by taking out a GCF of $-4rs$: $$-4rs(2r^{2}+3rs-5s^{2})$$ Put this back over the denominator: $$\frac{-4rs(2r^{2}+3rs-5s^{2}}{-4rs}$$ Finally, remove what cancels out to get the final answer: $$2r^{2}+3rs-5s^{2}$$
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