Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 1 - Section 1.4 - Rational Expressions - 1.4 Exercises: 80

Answer

$\dfrac{2x(x+6)^{4}-x^{2}(4)(x+6)^{3}}{(x+6)^{8}}=\dfrac{2x(6-x)}{(x+6)^{5}}$

Work Step by Step

$\dfrac{2x(x+6)^{4}-x^{2}(4)(x+6)^{3}}{(x+6)^{8}}$ Take out common factor $2x(x+6)^{3}$ from the numerator and simplify: $\dfrac{2x(x+6)^{4}-x^{2}(4)(x+6)^{3}}{(x+6)^{8}}=\dfrac{2x(x+6)^{3}[(x+6)-2x]}{(x+6)^{8}}=...$ $...=\dfrac{2x(x+6)^{3}(-x+6)}{(x+6)^{8}}=\dfrac{2x(6-x)}{(x+6)^{5}}$
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