Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 8 Rational Functions - 8.6 Solve Rational Equations - 8.6 Exercises - Skill Practice - Page 593: 16



Work Step by Step

In order to solve this equation, we find the common denominator of the two fractions. However, instead of trying to combine the fractions, we multiply both sides of the equation by this denominator. Doing this, we find: $$\frac{5}{x}x\left(x+3\right)-2x\left(x+3\right)=\frac{2}{x+3}x\left(x+3\right) \\ 5\left(x+3\right)-2x\left(x+3\right)=2x \\ x=-\frac{3+\sqrt{129}}{4},\:x=\frac{\sqrt{129}-3}{4}$$ Checking, we see that the solution is not extraneous.
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