Write the Form of the Partial Fraction Decomposition of the Rational

question 49

Multiple Choice

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { 4 } { x ^ { 2 } - 3 x }$

• A) \(\frac { A } { x } + \frac { B } { x - 3 }\)
• B) \(\frac { A } { x } + \frac { B } { 4 ( x + 3 ) }\)
• C) \(\frac { 1 } { x } + \frac { 1 } { x - 3 } + \frac { 1 } { x + 3 }\)
• D) \(\frac { A } { x ^ { 2 } - 3 x } + \frac { B } { 4 ( x - 4 ) }\)
• E) \(\frac { A } { 4 x } - \frac { B } { x - 3 }\)

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Definitions:

Generative

In various fields, generative denotes the capacity to produce or create something, often in a way that can spontaneously derive complex structures from simpler rules.

Semantic

Relates to the meanings of words and phrases in language.

Semantics

The study of meaning in language, focusing on the relationship between signifiers, like words, phrases, signs, and symbols, and what they stand for.

Syntax

A set of rules for arranging words and phrases to create well-formed sentences in a language.