Write the partial fraction decomposition of the rational expression.
-$$\frac { - 4 x ^ { 2 } - 6 x + 2 } { ( x + 2 ) ( x + 1 ) ^ { 2 } }$$
A) $\frac { - 2 } { x + 2 } + \frac { - 2 } { x + 1 } + \frac { 4 } { ( x + 1 ) ^ { 2 } }$
B) $\frac { 2 } { x + 2 } + \frac { - 2 } { x + 1 } + \frac { - 4 } { ( x + 1 ) ^ { 2 } }$
C) $\frac { 4 } { x + 2 } + \frac { - 2 } { x + 1 } + \frac { 2 } { ( x + 1 ) ^ { 2 } }$
D) $\frac { - 2 } { x + 2 } + \frac { 2 } { x + 1 } + \frac { 4 } { ( x + 1 ) ^ { 2 } }$

Question

Quizplus · Accepted Answer

The correct partial fraction decomposition is obtained by expressing the given rational expression as a sum of fractions whose denominators are the factors of the original denominator. In this case, the decomposition involves terms with denominators $x+2$, $x+1$, and $(x+1)^2$, and the coefficients are determined by algebraic manipulation to match the original expression.

Write the Partial Fraction Decomposition of the Rational Expression −4x2−6x+2(x+2)(x+1)2\frac { - 4 x ^ { 2 } - 6 x + 2 } { ( x + 2 ) ( x + 1 ) ^ { 2 } }(x+2)(x+1)2−4x2−6x+2​

Write the Partial Fraction Decomposition of the Rational Expression $\frac { - 4 x ^ { 2 } - 6 x + 2 } { ( x + 2 ) ( x + 1 ) ^ { 2 } }$