Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 8 - Rational Functions - 8-5 Adding and Subtracting Rational Expressions - Practice and Problem-Solving Exercises - Page 539: 27

Answer

$\dfrac{3x}{2 + xy}$

Work Step by Step

Do the addition in the denominator first. Find the least common denominator (LCD) of the two terms of the denominator: $\dfrac{3}{\frac{2}{x} + \frac{xy}{x}}$ Perform the addition in the denominator: $=\dfrac{3}{\frac{2 + xy}{x}}$ Rewrite this fraction as a division problem: $=3 \div \dfrac{2 + xy}{x}$ To divide one fraction by another, multiply the first fraction by the reciprocal of the second fraction: $=3 \times \dfrac{x}{2 + xy}$ Multiply to simplify: $=\dfrac{3x}{2 + xy}$
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