Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 7 - Functions and Graphs - 7.5 Formulas, Applications, and Variation - 7.5 Exercise Set: 18

Answer

$R=\frac{r_1r_2}{r_2+r_1}$

Work Step by Step

Eliminate the fractions by multiplying the LCD $Rr_1r_2$ to both sides of the equation: $\require{cancel} Rr_1r_2\left(\frac{1}{R}\right)=Rr_1r_2\left(\frac{1}{r_1} + \frac{1}{r_2}\right) \\\cancel{R}r_1r_2\left(\frac{1} {\cancel{R}}\right)=Rr_1r_2\left(\frac{1}{r_1}\right) + Rr_1r_2\left(\frac{1}{r_2}\right) \\r_1r_2=R\cancel{r_1}r_2\left(\frac{1}{\cancel{r_1}}\right) + Rr_1\cancel{r_2}\left(\frac{1}{\cancel{r_2}}\right) \\r_1r_2=Rr_2+Rr_1$ Factor out $R$: $r_1r_2=R(r_2+r_1)$ Divide $(r_2+r_1)$ to both sides: $\frac{r_1r_2}{r_2+r_1}=\frac{R(r_2+r_1)}{r_2+r_1} \\\frac{r_1r_2}{r_2+r_1}=R$
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