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: 77

Answer

$\dfrac{5}{x^{2}-4}+\dfrac{2}{x^{2}-4x+4}-\dfrac{3}{x^{2}-x-6}=\dfrac{4x^{2}-15x+6}{(x-2)^{2}(x+2)(x-3)}$

Work Step by Step

$\dfrac{5}{x^{2}-4}+\dfrac{2}{x^{2}-4x+4}-\dfrac{3}{x^{2}-x-6}$ Factor the three rational expressions completely: $\dfrac{5}{(x-2)(x+2)}+\dfrac{2}{(x-2)^{2}}-\dfrac{3}{(x-3)(x+2)}=...$ Evaluate the indicated operations and simplify: $...=\dfrac{5(x-3)(x-2)+2(x+2)(x-3)-3(x-2)^{2}}{(x-2)^{2}(x+2)(x-3)}=...$ $...=\dfrac{5x^{2}-25x+30+2x^{2}-2x-12-3x^{2}+12x-12}{(x-2)^{2}(x+2)(x-3)}=...$ $...=\dfrac{4x^{2}-15x+6}{(x-2)^{2}(x+2)(x-3)}$
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