Write the Partial Fraction Decomposition of the Rational Expression $\frac { x ^ { 2 } } { x ^ { 4 } - 23 x ^ { 2 } - 50 }$

question 24

Multiple Choice

Write the partial fraction decomposition of the rational expression. $\frac { x ^ { 2 } } { x ^ { 4 } - 23 x ^ { 2 } - 50 }$

• A)​ \(\frac { 1 } { x ^ { 2 } } - \frac { 1 } { 6 } - \frac { x ^ { 2 } } { 10 }\)
• B) \(\frac { 1 } { 27 } \left( \frac { 2 } { x ^ { 2 } + 2 } + \frac { 5 } { 2 ( x - 5 ) } - \frac { 5 } { 2 ( x + 5 ) } \right)\)
• C) \(\frac { 1 } { 27 } \left( \frac { 2 } { x ^ { 2 } + 2 } + \frac { 5 ( x + 2 ) } { 2 ( x - 5 ) } + \frac { 5 } { 2 ( x - 5 ) } \right)\)
• D) \(\frac { 1 } { 27 } \left( \frac { 2 } { x ^ { 2 } + 2 } - \frac { 5 } { 2 ( x - 5 ) } + \frac { 5 } { 2 ( x + 5 ) } \right)\)
• E) \(\frac { 1 } { 27 } \left( \frac { 2 } { x ^ { 2 } + 2 } + \frac { 5 } { 2 ( x - 5 ) } - \frac { 5 } { 2 ( x + 5 ) } \right)\)

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Definitions:

Gastric Secretion

The process of producing and releasing fluids, including hydrochloric acid and digestive enzymes, by the stomach's lining.

Muscularis

A layer of muscle in the walls of hollow organs, such as the gastrointestinal tract, responsible for movement of the organ's contents.

Rugae

Folds or ridges found on internal organ surfaces to increase surface area for secretion and absorption.

Gastric Glands

Glands located in the lining of the stomach that produce gastric juice, including hydrochloric acid and digestive enzymes.