Find the Partial Fraction Decomposition for the Given Rational Expression

question 64

Multiple Choice

Find the partial fraction decomposition for the given rational expression. Use the technique of Gaussian
elimination to find A, B, and C.
- $$\frac { - 3 x ^ { 2 } + 7 x - 10 } { ( x + 2 ) ( x - 1 ) ^ { 2 } } = \frac { A } { x + 2 } + \frac { B } { x - 1 } - \frac { C } { ( x - 1 ) ^ { 2 } }$$

• A) \(\frac { - 4 } { x + 2 } + \frac { 1 } { x - 1 } - \frac { 2 } { ( x - 1 ) ^ { 2 } }\)
• B) \(\frac { - 4 } { x + 2 } + \frac { 2 } { x - 1 } - \frac { 2 } { ( x - 1 ) ^ { 2 } }\)
• C) \(\frac { 4 } { x + 2 } + \frac { 1 } { x - 1 } - \frac { 2 } { ( x - 1 ) ^ { 2 } }\)
• D) \(\frac { - 4 } { x + 2 } + \frac { 1 } { x - 1 } + \frac { 2 } { ( x - 1 ) ^ { 2 } }\)

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