Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 7 - Section 7.4 - Adding and Subtracting Rational Expressions with Different Denominators - Exercise Set: 31

Answer

$\dfrac{1}{x+3}-\dfrac{1}{(x+3)^{2}}=\dfrac{x+2}{(x+3)^{2}}$

Work Step by Step

$\dfrac{1}{x+3}-\dfrac{1}{(x+3)^{2}}$ Evaluate the substraction of the two rational expressions: $\dfrac{1}{x+3}-\dfrac{1}{(x+3)^{2}}=\dfrac{(x+3)^{2}-(x+3)}{(x+3)^{3}}=...$ Take out common factor $x+3$ from the numerator and simplify: $...=\dfrac{(x+3)[(x+3)-1]}{(x+3)^{3}}=\dfrac{x+3-1}{(x+3)^{2}}=\dfrac{x+2}{(x+3)^{2}}$
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