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: 33


The equation has one solution, -14.

Work Step by Step

$\frac{2r}{r-4}-2=\frac{4}{r+5}$ $(r-4)(r+5)(\frac{2r}{r-4}-2)=(r-4)(r+5)\frac{4}{r+5}$ $\frac{(r-4)(r+5)2r}{r-4}-2(r-4)(r+5)=(r-4)(r+5)\frac{4}{r+5}$ $2r(r+5)-2(r^2+r-20)=4(r-4)$ $2r^2+10r-2r^2-2r+40=4r-16$ $8r+40=4r-16$ $4r=-56$ $r=-14$ Check: $-(2\times14)/(-14-4)-2=14/9-2=-4/9; 4/(-14+5)=-4/9$ The equation has one solution, -14.
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