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: 33

Answer

$\dfrac{4}{x^{2}+4x+3}+\dfrac{3}{x^{2}-x-2}=\dfrac{7x+1}{(x+1)(x+3)(x-2)}$

Work Step by Step

$\dfrac{4}{x^{2}+4x+3}+\dfrac{3}{x^{2}-x-2}$ Factor the denominators of both fractions: $\dfrac{4}{x^{2}+4x+3}+\dfrac{3}{x^{2}-x-2}=...$ $...=\dfrac{4}{(x+3)(x+1)}+\dfrac{3}{(x-2)(x+1)}=...$ Evaluate the sum of these two fractions using the LCD, which is $(x+1)(x+3)(x-2)$ in this case: $...=\dfrac{4(x-2)+3(x+3)}{(x+1)(x+3)(x-2)}=...$ Simplify: $...=\dfrac{4x-8+3x+9}{(x+1)(x+3)(x-2)}=...$ $...=\dfrac{7x+1}{(x+1)(x+3)(x-2)}$
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