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) $\frac { - 4 } { x + 2 } + \frac { 1 } { x - 1 } + \frac { 2 } { ( x - 1 ) ^ { 2 } }$

Question

Quizplus · Accepted Answer

The correct partial fraction decomposition is $\frac { - 4 } { x + 2 } + \frac { 1 } { x - 1 } - \frac { 2 } { ( x - 1 ) ^ { 2 } }$ because when you combine these fractions over a common denominator and simplify, you get the original expression.

Find the Partial Fraction Decomposition for the Given Rational Expression