Find the partial fraction decomposition for the rational expression.
-$$\frac { 4 x ^ { 2 } - 3 x + 2 } { \left( x ^ { 2 } - 4 \right) ( x - 1 ) }$$
A) $\frac { 3 } { x - 2 } + \frac { 2 } { x + 2 } + \frac { - 1 } { x - 1 }$

B) $\frac { 5 } { x - 2 } + \frac { 3 } { x + 2 } + \frac { - 2 } { x - 1 }$

C) $\frac { 5 } { x ^ { 2 } - 4 } + \frac { - 1 } { x - 1 }$

D) $\frac { 2 } { x - 2 } + \frac { 3 } { x + 2 } + \frac { 1 } { x - 1 }$

Question

Find the partial fraction decomposition for the rational expression.
-$$\frac { 4 x ^ { 2 } - 3 x + 2 } { \left( x ^ { 2 } - 4 \right) ( x - 1 ) }$$
A) $\frac { 3 } { x - 2 } + \frac { 2 } { x + 2 } + \frac { - 1 } { x - 1 }$

B) $\frac { 5 } { x - 2 } + \frac { 3 } { x + 2 } + \frac { - 2 } { x - 1 }$

C) $\frac { 5 } { x ^ { 2 } - 4 } + \frac { - 1 } { x - 1 }$

D) $\frac { 2 } { x - 2 } + \frac { 3 } { x + 2 } + \frac { 1 } { x - 1 }$

Quizplus · Accepted Answer

The denominator $(x^2 - 4)(x - 1)$ factors into $(x - 2)(x + 2)(x - 1)$, indicating the need for partial fractions of the form $\frac{A}{x - 2} + \frac{B}{x + 2} + \frac{C}{x - 1}$. Solving for A, B, and C using the given numerator $4x^2 - 3x + 2$ leads to the coefficients in option A.

Find the Partial Fraction Decomposition for the Rational Expression 4x2−3x+2(x2−4)(x−1)\frac { 4 x ^ { 2 } - 3 x + 2 } { \left( x ^ { 2 } - 4 \right) ( x - 1 ) }(x2−4)(x−1)4x2−3x+2​

Find the Partial Fraction Decomposition for the Rational Expression $\frac { 4 x ^ { 2 } - 3 x + 2 } { \left( x ^ { 2 } - 4 \right) ( x - 1 ) }$