Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 7 - Section 7.7 - Simplifying Complex Fractions - Exercise Set: 33

Answer

$\dfrac{3+\dfrac{12}{x}}{1-\dfrac{16}{x^{2}}}=\dfrac{3x}{x-4}$

Work Step by Step

$\dfrac{3+\dfrac{12}{x}}{1-\dfrac{16}{x^{2}}}$ Evaluate the sum indicated in the numerator and the substraction indicated in the denominator: $\dfrac{3+\dfrac{12}{x}}{1-\dfrac{16}{x^{2}}}=\dfrac{\dfrac{3x+12}{x}}{\dfrac{x^{2}-16}{x^{2}}}=...$ Evaluate the division: $...=\dfrac{3x+12}{x}\div\dfrac{x^{2}-16}{x^{2}}=\dfrac{x^{2}(3x+12)}{x(x^{2}-16)}=...$ Take out common factor $3$ from the parentheses in the numerator and factor the denominator: $...=\dfrac{3x^{2}(x+4)}{x(x-4)(x+4)}=...$ Simplify: $...=\dfrac{3x^{2}}{x(x-4)}=\dfrac{3x}{x-4}$
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