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

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

Quizplus · Accepted Answer

The partial fraction decomposition of the given rational expression is obtained by expressing it as a sum of fractions whose denominators are the factors of the original denominator. The correct decomposition is $\frac { - 2 } { x + 2 } + \frac { - 2 } { x + 1 } + \frac { 4 } { ( x + 1 ) ^ { 2 } }$, which matches option A. This is determined by solving a system of equations that arises from equating the original expression to the proposed decomposition and solving for the coefficients.

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 $\frac { - 4 x ^ { 2 } - 6 x + 2 } { ( x + 2 ) ( x + 1 ) ^ { 2 } }$