Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 6 - Rational Expressions and Equations - 6.3 Addition, Subtraction, and Least Common Denominators - 6.3 Exercise Set: 25

Answer

$\dfrac{1}{x+2}$

Work Step by Step

Adding the numerators and copying the denominator, the given expression, $ \dfrac{x-6}{x^2+5x+6}+\dfrac{9}{x^2+5x+6} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{x-6+9}{x^2+5x+6} \\\\= \dfrac{x+3}{x^2+5x+6} \\\\= \dfrac{x+3}{(x+3)(x+2)} \\\\= \dfrac{\cancel{x+3}}{(\cancel{x+3})(x+2)} \\\\= \dfrac{1}{x+2} .\end{array}
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