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: 94

Answer

$\frac{23}{18}x+\frac{29}{20}y$

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 the fractions) to obtain: $\frac{5}{6}x+\frac{3}{4}y+\frac{4}{9}x+\frac{7}{10}y$ =$x(\frac{5}{6}+\frac{4}{9})+y(\frac{3}{4}+\frac{7}{10})$ =$x(\frac{5(3)+4(2)}{18})+y(\frac{3(5)+7(2)}{20})$ =$x(\frac{15+8}{18})+y(\frac{15+14}{20})$ =$x(\frac{23}{18})+y(\frac{29}{20})$ =$\frac{23}{18}x+\frac{29}{20}y$
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