Intermediate Algebra (6th Edition)

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

Chapter 6 - Section 6.3 - Simplifying Complex Fractions - Exercise Set: 34

Answer

$2$

Work Step by Step

The given expression, $ \dfrac{\dfrac{2}{x+2}+\dfrac{6}{x+7}}{\dfrac{4x+13}{x^2+9x+14}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\dfrac{2(x+7)+6(x+2)}{(x+2)(x+7)}}{\dfrac{4x+13}{(x+2)(x+7)}} \\\\= \dfrac{\dfrac{2(x+7)+6(x+2)}{\cancel{(x+2)(x+7)}}}{\dfrac{4x+13}{\cancel{(x+2)(x+7)}}} \\\\= \dfrac{2(x+7)+6(x+2)}{4x+13} \\\\= \dfrac{2x+14+6x+12}{4x+13} \\\\= \dfrac{8x+26}{4x+13} \\\\= \dfrac{2(4x+13)}{4x+13} \\\\= \dfrac{2(\cancel{4x+13})}{\cancel{4x+13}} \\\\= 2 .\end{array}
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