Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Section P.6 - Rational Expressions - Exercise Set - Page 87: 116


The required solution is False

Work Step by Step

We have the given algebraic expression: $6+\frac{1}{x}=\frac{7}{x}$ We know that for an algebraic expression, a rational expression is an expression which can be expressed in the form $\frac{p}{q}$, where, both $p\ \text{and }q$ are polynomials and the denominator $q\ne 0$. Now, solve the left-hand side of the given algebraic expression: $\begin{align} & 6+\frac{1}{x}=6\times \frac{x}{x}+\frac{1}{x} \\ & =\frac{6x}{x}+\frac{1}{x} \\ & =\frac{6x+1}{x} \end{align}$ Thus, $6+\frac{1}{x}=\frac{6x+1}{x}$. Hence, the given statement is False.
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