Write the Partial Fraction Decomposition of the Rational Expression $\frac { 7 x - 8 } { ( x - 1 ) ^ { 2 } }$

question 136

Multiple Choice

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 7 x - 8 } { ( x - 1 ) ^ { 2 } }$

• A) \(\frac { 7 } { x - 1 } + \frac { 1 } { ( x + 1 ) ^ { 3 } }\)
• B) \(\frac { 7 } { x - 1 } - \frac { 1 } { ( x + 1 ) ^ { 2 } }\)
• C) \(\frac { 7 } { ( x - 1 ) ^ { 2 } } - \frac { 1 } { ( x - 1 ) ^ { 3 } }\)
• D) \(\frac { 7 } { x - 1 } - \frac { 1 } { ( x - 1 ) ^ { 2 } }\)
• E) \(\frac { 7 } { x - 1 } + \frac { 1 } { ( x - 1 ) ^ { 2 } }\)

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Definitions:

Quantity

The measure or number of units of a particular material or immaterial entity.

Conjunctive

Pertaining to conditions or tasks that require collective effort and cooperation, where the group's success is limited by its least capable member.

Disjunctive

Refers to a situation or task requiring a solution that can come from any single group member who possesses the necessary knowledge, solving the problem more efficiently than others.

Compensatory

Compensatory refers to something designed to counterbalance or make up for a deficiency or lack.