Write the Partial Fraction Decomposition of the Rational Expression $\frac { 1 } { x ^ { 2 } - 16 }$

question 39

Multiple Choice

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ $\frac { 1 } { x ^ { 2 } - 16 }$ ​

• A) \(\frac { 1 } { 8 } \left( \frac { A } { x - 4 } - \frac { B } { x + 4 } \right)\)
• B) \(\frac { 8 } { x - 4 } - \frac { 8 } { x + 4 }\)
• C) \(\frac { 1 } { 8 } \left( \frac { 8 } { x - 4 } - \frac { 8 } { x + 4 } \right)\)
• D) \(\frac { 1 } { 8 } \left( \frac { 1 } { x - 4 } - \frac { 1 } { x + 4 } \right)\)
• E) \(\frac { 1 } { 8 } \left( \frac { 1 } { x - 4 } + \frac { 1 } { x + 4 } \right)\)

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Definitions:

Pre-Attachment

The initial stage in an infant’s development of attachment, characterized by indiscriminate sociability and the formation of initial bonds with caregivers.

Attachment Type

This refers to the classification of an individual's patterns of attachment in relationships, which can significantly affect their interpersonal relationships and behavior.

Insecure-Avoidant Attachment

A pattern in child development where the child shows a preference for self-sufficiency, often avoiding or showing indifference towards caregivers.

Strange Situation

A structured laboratory procedure that measures the security of attachment by observing infants’ reactions to being separated from the caregiver in an unfamiliar environment.