Write the Partial Fraction Decomposition of the Rational Expression $$\frac { x + 2 } { x ^ { 3 } - 2 x ^ { 2 } + x }$$

question 108

Multiple Choice

Write the partial fraction decomposition of the rational expression.
- $$\frac { x + 2 } { x ^ { 3 } - 2 x ^ { 2 } + x }$$

• A) \(\frac { 2 } { x } + \frac { - 2 } { x - 1 } + \frac { 3 } { ( x - 1 ) ^ { 2 } }\)
• B) \(\frac { 2 } { x } + \frac { 3 } { x - 1 } + \frac { - 2 } { ( x - 1 ) ^ { 2 } }\)
• C) \(\frac { 2 } { x } + \frac { - 2 } { x - 1 } + \frac { 5 } { ( x - 1 ) ^ { 2 } }\)
• D) \(\frac { - 2 } { x } + \frac { 2 } { x - 1 } + \frac { 3 } { ( x - 1 ) ^ { 2 } }\)

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Definitions:

Perilymph

The fluid that fills the space within the inner ear between the cochlea and the vestibular system, aiding in hearing and balance.

Bony Labyrinth

A complex system of passages and cavities within the temporal bone of the skull, important for hearing and balance.

Membranous Labyrinth

A complex system of fluid-filled tubes and sacs located within the inner ear, crucial for hearing and balance.

Auditory Tube

A tube that connects the middle ear to the nasopharynx, helping to equalize pressure in the ear.