College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Section P.8 - Solving Basic Equations - P.8 Exercises - Page 60: 54


The solution is all real numbers except $x=0$ and $x=-1/2$.

Work Step by Step

$\displaystyle \frac{1}{x}-\frac{2}{2x+1}=\frac{1}{2x^{2}+x}$ We multiply both sides by $(2x+1)(x)$: $(2x+1)-2(x)=1$ And distribute: $1=1$ When we get an identity (1=1, 2=2, x=x, etc), this implies that no matter what we choose for $x$, we will get a solution. Thus the solution should be all real numbers. However, if we use $x=0$ or $x=-1/2$, we would get division by 0 in the original equation. So these values are not allowed. Thus the solution is all real numbers except $x=0$ and $x=-1/2$.
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