Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 3 - Section 3.7 - Polynomial and Rational Inequalities - 3.7 Exercises - Page 316: 26

Answer

$(-4, -2) U (2, 4)$

Work Step by Step

$\frac{x^2 - 16}{x^4 - 16} < 0$ $\frac{(x-4)(x+4)}{(x^2 - 4) (x^2 + 4)} < 0$ $\frac{(x-4)(x+4)}{(x-2)(x+2)(x^2+4)} < 0$ Find the zeros of the expressions in the numerator AND the denominator $x = -2, 2, 4, -4$ Test numbers in between those zero values to determine if the function is negative or positive $(-∞, -4)$ $\frac{(-)(-))}{(-)(-)(+)} = (+)$ $(-4, -2])$ $\frac{(-)(+)}{(-)(-)(+)} = (-)$ $(-2, 2)$ $\frac{(-)(+)}{(-)(+)(+)} = (+)$ $(2, 4)$ $\frac{(-)(+)}{(+)(+)(+)} = (-)$ $(4, ∞)$ $\frac{(+)(+)}{(+)(+)(+))} = (+)$ Thus the solution is $(-4, -2) U (2, 4)$
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