Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 6 - Test: 12

Answer

$\dfrac{5x-2}{(x-3)(x+2)(x-2)}$

Work Step by Step

The given expression, $ \dfrac{3}{x^2-x-6}+\dfrac{2}{x^2-5x+6} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{3}{(x-3)(x+2)}+\dfrac{2}{(x-2)(x-3)} \\\\= \dfrac{(x-2)(3)+(x+2)(2)}{(x-3)(x+2)(x-2)} \\\\= \dfrac{3x-6+2x+4}{(x-3)(x+2)(x-2)} \\\\= \dfrac{5x-2}{(x-3)(x+2)(x-2)} .\end{array}
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