Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter R - Algebra Reference - R.3 Rational Expressions - R.3 Exercises: 37

Answer

$\dfrac{2}{a+2}+\dfrac{1}{a}+\dfrac{a-1}{a^{2}+2a}=\dfrac{4a+1}{a(a+2)}$

Work Step by Step

$\dfrac{2}{a+2}+\dfrac{1}{a}+\dfrac{a-1}{a^{2}+2a}$ Take out common factor $a$ from the denominator of the third fraction: $\dfrac{2}{a+2}+\dfrac{1}{a}+\dfrac{a-1}{a^{2}+2a}=...$ $...=\dfrac{2}{a+2}+\dfrac{1}{a}+\dfrac{a-1}{a(a+2)}=...$ Evaluate the sum of the three rational expressions by using the LCD, which is $a(a+2)$ in this case: $...=\dfrac{2a+a+2+a-1}{a(a+2)}=...$ Simplify: $...=\dfrac{4a+1}{a(a+2)}$
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