Find the Partial Fraction Decomposition for the Rational Expression $\frac { 2 x ^ { 3 } - 7 x ^ { 2 } + 5 x - 3 } { x ^ { 2 } + x - 2 }$

question 409

Multiple Choice

Find the partial fraction decomposition for the rational expression.
$\frac { 2 x ^ { 3 } - 7 x ^ { 2 } + 5 x - 3 } { x ^ { 2 } + x - 2 }$

• A) \(2 x - 9 + \frac { 19 } { x + 2 } - \frac { - 1 } { x - 1 }\)
• B) \(2 x + 9 + \frac { - 13 } { x + 2 } + \frac { 7 } { x - 1 }\)
• C) \(2 x + 5 + \frac { - 7 / 3 } { x + 2 } + \frac { 13 / 3 } { x - 1 }\)
• D) \(2 x - 9 + \frac { - 5 / 3 } { x + 2 } + \frac { 1 / 3 } { x - 1 }\)

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Definitions:

Chemical Digestion

The breakdown of complex food molecules into simpler ones through chemical reactions, involving enzymes and other digestive substances.

Lacteal

Lymphatic vessel in an intestinal villus; aids in the absorption of fats.

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Fats are a group of organic compounds that are insoluble in water, serve as a major energy source for the body, and are crucial for cell structure and function.

Serosa

A smooth membrane consisting of a layer of cells that secretes serous fluid, covering the outermost layer of various organs within the body cavities.