Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 1 - Review - Exercises: 44

Answer

$\dfrac{x^{2}-2x-15}{x^{2}-6x+5}\div\dfrac{x^{2}-x-12}{x^{2}-1}=\dfrac{x+1}{x-4}$

Work Step by Step

$\dfrac{x^{2}-2x-15}{x^{2}-6x+5}\div\dfrac{x^{2}-x-12}{x^{2}-1}$ Factor both rational expressions completely: $\dfrac{x^{2}-2x-15}{x^{2}-6x+5}\div\dfrac{x^{2}-x-12}{x^{2}-1}=...$ $...=\dfrac{(x-5)(x+3)}{(x-5)(x-1)}\div\dfrac{(x-4)(x+3)}{(x-1)(x+1)}=...$ Evaluate the division of the two fractions and simplify by removing the factors that appear both in the numerator and in the denominator of the resulting rational expression: $...=\dfrac{(x-5)(x+3)(x-1)(x+1)}{(x-5)(x-1)(x-4)(x+3)}=...$ $...=\dfrac{x+1}{x-4}$
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