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: 95

Answer

$-\frac{11}{45}x-\frac{9}{20}y$

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: $\frac{2}{9}x+\frac{5}{12}y-\frac{7}{15}x-\frac{13}{15}y$ =$x(\frac{2}{9}-\frac{7}{15})+y(\frac{5}{12}-\frac{13}{15})$ =$x(\frac{2(5)-7(3)}{45})+y(\frac{5(5)-13(4)}{60})$ =$x(\frac{10-21}{45})+y(\frac{25-52}{60})$ =$x(\frac{-11}{45})+y(\frac{-27}{60})$ =$-\frac{11}{45}x-\frac{9}{20}y$
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