Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 1 - Section 1.5 - Equations - 1.5 Exercises: 34

Answer

$R_1 = \frac{RR_2}{R_2 - R}$

Work Step by Step

$Solve$ $the$ $equation$ $for$ $the$ $indicated$ $variable:$ $\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2};$ $for$ $R_1$ Solve for $R_1$ Subtract $\frac{1}{R_2}$ from both sides $\frac{1}{R} - \frac{1}{R_2} = \frac{1}{R_1} + \frac{1}{R_2} - \frac{1}{R_2}$ Simplify $\frac{1}{R} - \frac{1}{R_2} = \frac{1}{R_1}$ $\frac{1}{R_1} = \frac{1}{R} - \frac{1}{R_2}$ Combine the right side to a single fraction by finding the common denominator $(RR_2)$ $\frac{1}{R_1} = \frac{1\times R_2}{R\times R_2} - \frac{1\times R}{R_2\times R}$ $\frac{1}{R_1} = \frac{R_2 - R}{RR_2}$ Cross Multiply between both sides $R_1 (R_2 - R) = 1 (RR_2)$ Divide both sides by $(R_2 - R)$ $\frac{R_1(R_2 - R)}{R_2 - R} = \frac{RR_2}{R_2 - R}$ $R_1 = \frac{RR_2}{R_2 - R}$
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