Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter R - Review of Basic Concepts - R.6 Rational Exponents - R.6 Exercises - Page 65: 116

Answer

$\frac{20t+8}{(3t+1)^{3/2}}$

Work Step by Step

Start with cancelling the common factor $(3t+1)^{-3/4}$, we have: $\frac{7(3t+1)^{1/4}-(t-1)(3t+1)^{-3/4}}{(3t+1)^{3/4}}=\frac{7(3t+1)^{1/4+3/4}-(t-1)}{(3t+1)^{3/4+3/4}}=\frac{7(3t+1)-(t-1)}{(3t+1)^{3/2}}=\frac{20t+8}{(3t+1)^{3/2}}$
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