## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 7 - Section 7.3 - Partial Fractions - Exercise Set - Page 841: 4

#### Answer

The partial fraction expansion is $\frac{3x+16}{\left( x+1 \right){{\left( x-2 \right)}^{2}}}=\frac{A}{\left( x+1 \right)}+\frac{B}{\left( x-2 \right)}+\frac{C}{{{\left( x-2 \right)}^{2}}}$.

#### Work Step by Step

The provided partial expression is as given below: $\frac{3x+16}{\left( x+1 \right){{\left( x-2 \right)}^{2}}}$ Now, solve the expression as follows: We set up the partial fraction expansion with unknown constants coefficients and then write a constant coefficients over each of the two distinct algebraic linear factors in the denominator of the expression. $\frac{3x+16}{\left( x+1 \right){{\left( x-2 \right)}^{2}}}=\frac{A}{\left( x+1 \right)}+\frac{B}{\left( x-2 \right)}+\frac{C}{{{\left( x-2 \right)}^{2}}}$ Thus, $\frac{A}{\left( x+1 \right)}+\frac{B}{\left( x-2 \right)}+\frac{C}{{{\left( x-2 \right)}^{2}}}$ is a partial fraction expansion of the rational expression $\frac{3x+16}{\left( x+1 \right){{\left( x-2 \right)}^{2}}}$ with constants $A$, $B$ and $C$.

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