Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 11 - Section 11.1 - Sequences and Summation Notation - Exercise Set - Page 831: 97


The solution set is $\left \{-\frac{6}{5},4 \right \}$.

Work Step by Step

The given expression is $\frac{6}{x}+\frac{6}{x+2}=\frac{5}{2}$ The lowest common multiple of denominators is $2x(x+2)$ Multiply all fractions by lowest common multiple. $[2x(x+2)]\frac{6}{x}+[2x(x+2)]\frac{6}{x+2}=[2x(x+2)]\frac{5}{2}$ Simplify. $12(x+2)+12x=5x(x+2)$ Clear the parentheses. $12x+24+12x=5x^2+10x$ $24+24x=5x^2+10x$ $0=5x^2+10x-24x-24$ $0=5x^2+14x-24$ Factor. $0=5x^2+6x-20x-24$ $0=x(5x+6)-4(5x+6)$ $0=(5x+6)(x-4)$ Equate both factors equal to zero. $5x+6=0$ or $x-4=0$ $5x=-6$ or $x=4$ $x=-\frac{6}{5}$ or $x=4$.
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