Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 2 - Real Numbers - 2.2 - Addition and Subtraction of Rational Numbers - Problem Set 2.2: 93

Answer

$\frac{13}{14}x+\frac{9}{8}y$

Work Step by Step

We first factor out $x$ and $y$. Then, to simplify this expression, we find the common denominator (which is the LCM of the denominators of all of the fractions) to obtain: $\frac{3}{7}x+\frac{1}{4}y+\frac{1}{2}x+\frac{7}{8}y$ =$x(\frac{3}{7}+\frac{1}{2})+y(\frac{1}{4}+\frac{7}{8})$ $x(\frac{3}{7}+\frac{1}{2})+y(\frac{1}{4}+\frac{7}{8})$ =$x(\frac{3(2)+7(1)}{14})+y(\frac{1(2)+7(1)}{8})$ =$x(\frac{6+7}{14})+y(\frac{2+7}{8})$ =$x(\frac{13}{14})+y(\frac{9}{8})$ =$\frac{13}{14}x+\frac{9}{8}y$
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