Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 11 - Rational Expressions and Functions - 11-5 Solving Rational Equations - Practice and Problem-Solving Exercises - Page 696: 34

Answer

The equation has one solution, 3.

Work Step by Step

$\frac{r+1}{r-1}=\frac{r}{3}+\frac{2}{r-1}$ $3(r-1)\frac{r+1}{r-1}=3(r-1)(\frac{r}{3}+\frac{2}{r-1})$ $3(r+1)=\frac{3(r-1)r}{3}+\frac{6(r-1)}{r-1}$ $3r+3=r(r-1)+6$ $3r+3=r^2-r+6$ $r^2-4r+3=0$ $(r-1)(r-3)=0$ $r-1=0$ or $r-3=0$ $r=1$ or $r=3$ Check: $(1+1)/(1-1)=2/0$ (undefined) $(3+1)/(3-1)=4/2=2; 3/3+2/(3-1)=1+1=2$ The equation has one solution, 3.
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