Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 10 - Quadratic Equations - 10.4 - Solving Quadratic Equations - Which Method? - Problem Set 10.4 - Page 458: 34



Work Step by Step

First, we add the fractions on the left hand side by taking their LCM. Upon inspection, the LCM is found to be $x$: $x+\frac{1}{x}=\frac{65}{8}$ $\frac{x(x)+1(1)}{x}=\frac{65}{8}$ $\frac{x^{2}+1}{x}=\frac{65}{8}$ Now, we cross multiply the two fractions in order to create a quardratic equation: $\frac{x^{2}+1}{x}=\frac{65}{8}$ $8(x^{2}+1)=65(x)$ $8x^{2}+8=65x$ $8x^{2}-65x+8=0$ Now, we use rules of factoring trinomials to solve the equation: $8x^{2}-65x+8=0$ $8x^{2}-1x-64x+8=0$ $x(8x-1)-8(8x-1)=0$ $(8x-1)(x-8)=0$ $(8x-1)=0$ or $(x-8)=0$ $x=\frac{1}{8}$ or $x=8$ Therefore, the solution is {$\frac{1}{8},8$}.
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