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: 79

Answer

$-\dfrac{2x^{2}-14x-55}{(x+7)(x+2)(x+3)}$

Work Step by Step

$\dfrac{9}{x^{2}+9x+14}-\dfrac{3x}{x^{2}+10x+21}+\dfrac{x+4}{x^{2}+5x+6}$ Factor all three rational expressions completely: $\dfrac{9}{(x+7)(x+2)}-\dfrac{3x}{(x+7)(x+3)}+\dfrac{x+4}{(x+3)(x+2)}=...$ Evaluate the indicated operations and simplify: $...=\dfrac{9(x+3)-3x(x+2)+(x+4)(x+7)}{(x+7)(x+2)(x+3)}=...$ $...=\dfrac{9x+27-3x^{2}-6x+x^{2}+11x+28}{(x+7)(x+2)(x+3)}=...$ $...=\dfrac{-2x^{2}+14x+55}{(x+7)(x+2)(x+3)}=-\dfrac{2x^{2}-14x-55}{(x+7)(x+2)(x+3)}$
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