The partial fraction decomposition of \dfrac{-x^2 + 8x + 8}{x^3 + 4x^2 + 4x + 16} can be written...
Question:
The partial fraction decomposition of {eq}\dfrac{-x^2 + 8x + 8}{x^3 + 4x^2 + 4x + 16} {/eq} can be written in the form of {eq}\dfrac{f(x)}{x + 4} + \dfrac{g(x)}{x^2 + 4} {/eq} where
{eq}f(x) = \enspace \rule{2cm}{0.4pt} \\ g(x) = \enspace \rule{2cm}{0.4pt} {/eq}
Partial Decomposition of Rational Function:
The degree of the numerator must always be lower than the degree of the denominator when splitting a rational function into partial fractions. It is possible to combine repeated and non-repeated linear and quadratic components in the denominator.
Answer and Explanation: 1
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Given:
- The rational expression given is {eq}\dfrac{{ - {x^2} + 8x + 8}}{{{x^3} + 4{x^2} + 4x + 16}} {/eq}.
The objective is to evaluate the...
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Chapter 3 / Lesson 26Learn about what partial fractions are and their formula. Understand the method of how to do partial fractions from the rational and improper functions.