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: 114


The required solution is True

Work Step by Step

We have the given algebraic expression: $\frac{-3y-6}{y+2}$ 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, factorize the numerator of the given expression: $-3y-6=-3\left( y+6 \right)$ So, the fraction gets simplified to the form: $\begin{align} & \frac{-3y-6}{y+2}=\frac{-3\left( y+2 \right)}{\left( y+2 \right)} \\ & =\frac{-3\left( y+2 \right)}{\left( y+2 \right)} \\ & =-3 \end{align}$ Thus, the result of the given algebraic expression simplifies to the consecutive integer that follows $-4$. Hence, the given statement is True.
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