Write the partial fraction decomposition of the rational expression.
-$$\frac { 6 x ^ { 2 } - x - 19 } { x ( x + 1 ) ( x - 1 ) }$$
A) $\frac { 19 } { x } + \frac { - 6 } { x + 1 } + \frac { - 7 } { x - 1 }$
B) $\frac { 19 } { x } + \frac { 6 } { x + 1 } + \frac { - 7 } { x - 1 }$
C) $\frac { 19 } { x } + \frac { - 6 } { x + 1 } + \frac { 7 } { x - 1 }$
D) $\frac { 19 } { x } + \frac { - 7 } { x + 1 } + \frac { 6 } { x - 1 }$

Question

Quizplus · Accepted Answer

The correct partial fraction decomposition involves finding constants A, B, and C such that $\frac{6x^2 - x - 19}{x(x+1)(x-1)} = \frac{A}{x} + \frac{B}{x+1} + \frac{C}{x-1}$. Solving for these constants gives A = 19, B = -6, and C = -7.

Write the Partial Fraction Decomposition of the Rational Expression 6x2−x−19x(x+1)(x−1)\frac { 6 x ^ { 2 } - x - 19 } { x ( x + 1 ) ( x - 1 ) }x(x+1)(x−1)6x2−x−19​

Write the Partial Fraction Decomposition of the Rational Expression $\frac { 6 x ^ { 2 } - x - 19 } { x ( x + 1 ) ( x - 1 ) }$