Find the Partial Fraction Decomposition for the Rational Expression $\frac { 2 x ^ { 3 } - 5 x ^ { 2 } - 1 x + 7 } { ( x - 1 ) ^ { 3 } ( x + 2 ) }$

question 206

Multiple Choice

Find the partial fraction decomposition for the rational expression.
$\frac { 2 x ^ { 3 } - 5 x ^ { 2 } - 1 x + 7 } { ( x - 1 ) ^ { 3 } ( x + 2 ) }$

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

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