Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 8 Rational Functions - 8.5 Add and Subtract Rational Expressions - 8.5 Exercises - Skill Practice - Page 586: 30

Answer

$\frac{-x^3-3x^2-x-51}{x^3+3x^2-25x-75}$

Work Step by Step

Write each rational expression using the least common denominators and then simplify: $\frac{x+3}{x^2-25}-\frac{x-1}{x-5}+\frac{3}{x+3}$ $=\frac{(x+3)(x+3)}{(x^2-5)(x+3)}-\frac{(x+5)(x-1)(x+3)}{(x+5)(x-5)(x+3)}+\frac{(x^2-25)(3)}{(x^2-25)(x+3)}$ $=\frac{x^2+6x+9}{(x+5)(x-5)(x+3)}-\frac{x^3+7x^2+7x-15}{(x+5)(x-5)(x-3)}+\frac{3x^2-75}{(x+5)(x-5)(x+3)}$ $=\frac{-x^3-3x^2-x-51}{x^3+3x^2-25x-75}$
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