Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter R - Algebra Reference - R.3 Rational Expressions - R.3 Exercises - Page R-10: 14


$ \displaystyle \frac{25p^{2}}{9}$

Work Step by Step

$\displaystyle \frac{15p^{3}}{9p^{2}}\div\frac{6p}{10p^{2}}= \qquad$... apply property:$ \displaystyle \frac{P}{Q}\div\frac{R}{S}=\frac{P}{Q}\cdot\frac{S}{R} $ $=\displaystyle \frac{15p^{3}}{9p^{2}}\cdot\frac{10p^{2}}{6p}= \qquad$... apply property: $\displaystyle \frac{P}{Q}\cdot\frac{R}{S}=\frac{PR}{QS}$ $...15=3\cdot 5,\quad 10=2\cdot 5,\quad$ $...9=3\cdot 3,\quad 6=2\cdot 3,\quad p^{5}=p^{3}p^{2}$ $=\displaystyle \frac{3\cdot 5\cdot 2\cdot 5p^{3}p^{2}}{3\cdot 3\cdot 2\cdot 3p^{3}}\qquad \qquad$... reduce: 3, 2, $p^{3}$ $= \displaystyle \frac{25p^{2}}{9}$
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