Find the Partial Fraction Decomposition for the Rational Expression $$\frac { x ^ { 2 } } { x ^ { 2 } + 6 x + 9 }$$

question 36

Multiple Choice

Find the partial fraction decomposition for the rational expression.
- $$\frac { x ^ { 2 } } { x ^ { 2 } + 6 x + 9 }$$

• A) \(\frac { 6 } { x + 3 } + \frac { - 6 } { ( x + 3 ) ^ { 2 } }\)
• B) \(\frac { - 6 } { x + 3 } + \frac { 9 } { ( x + 3 ) ^ { 2 } }\)
• C) \(1 + \frac { 6 } { x + 3 } + \frac { - 9 } { ( x + 31 ) ^ { 2 } }\)
• D) \(1 + \frac { - 6 } { x + 3 } + \frac { 9 } { ( x + 3 ) ^ { 2 } }\)

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Definitions:

Autonomic Motor Neurons

Nerve cells that control involuntary actions of the muscles and glands, part of the autonomic nervous system.

Reflex Arcs

The neural pathway that mediates a reflex action, involving receptors, sensory neurons, interneurons, motor neurons, and effectors.

Cerebral Cortex

The outer layer of neural tissue of the cerebrum in the brain, responsible for higher brain functions like thought and action.

Inhibitory Neurons

Neurons that reduce the activity of their target neurons, playing critical roles in regulating neural circuits.