Write the Form of the Partial Fraction Decomposition of the Rational

question 51

Multiple Choice

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { 7 x ^ { 2 } + 6 } { ( x - 6 ) ^ { 3 } }$

• A) \(\frac { A } { ( x - 6 ) ^ { 3 } }\)
• B) \(\frac { 7 } { x - 6 } + \frac { 6 } { x - 6 } + \frac { 6 } { x - 6 }\)
• C) \(\frac { A } { x - 6 } + \frac { B } { ( x - 6 ) ^ { 2 } }\)
• D) \(\frac { A } { x - 6 } + \frac { B } { ( x - 6 ) ^ { 2 } } + \frac { C } { ( x - 6 ) ^ { 3 } }\)
• E) \(\frac { A } { 6 ( x - 6 ) } - \frac { B } { 7 ( x - 6 ) ^ { 2 } } - \frac { C } { 7 ( x - 6 ) ^ { 3 } }\)

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Definitions:

Connective

In logic and linguistics, a term for words or phrases that link propositions and sentences together to form coherent text.

Predicate

The part of a sentence or clause that tells something about the subject, often relating to an action or attribute.

Nonrestrictive Clause

A type of clause that provides extra information about a noun in a sentence but does not limit its meaning.

Restrictive Clause

A clause that defines or limits the meaning of the noun it modifies and is essential to the meaning of a sentence.