Precalculus (6th Edition) Blitzer

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

Chapter 7 - Section 7.3 - Partial Fractions - Exercise Set - Page 842: 62


The provided statement does not make sense.

Work Step by Step

Let us consider, $\frac{7{{x}^{2}}+9x+3}{\left( x+5 \right)\left( {{x}^{2}}-3x+2 \right)}=\frac{A}{\left( x+5 \right)}+\frac{Bx+C}{\left( {{x}^{2}}-3x+2 \right)}$ Where, $P\left( x \right)=7{{x}^{2}}+9x+3$ and $Q\left( x \right)=\left( x+5 \right)\left( {{x}^{2}}-3x+2 \right)$ $\begin{align} & \frac{7{{x}^{2}}+9x+3}{\left( x+5 \right)\left( {{x}^{2}}-3x+2 \right)}=\frac{A}{\left( x+5 \right)}+\frac{Bx+C}{\left( {{x}^{2}}-3x+2 \right)} \\ & 7{{x}^{2}}+9x+3=A\left( {{x}^{2}}-3x+2 \right)+Bx\left( x+5 \right)+C\left( x+5 \right) \end{align}$ Therefore, the partial fraction does not make sense because the degree of $P\left( x \right)$ is less than the degree of $Q\left( x \right)$. Thus, this partial fraction does make sense.
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