Write the partial fraction decomposition of the rational expression.
-$$\frac { 14 x ^ { 2 } - 48 x - 54 } { x ( x - 6 ) ( x + 3 ) }$$
A) $\frac { 3 } { x } + \frac { 3 } { x - 6 } + \frac { 8 } { x + 3 }$
B) $\frac { 3 } { x } + \frac { 4 } { x - 6 } + \frac { 7 } { x + 3 }$
C) $\frac { 3 } { x } + \frac { 2 } { x - 6 } + \frac { 9 } { x + 3 }$
D) $\frac { x + 3 } { x ^ { 2 } - 6 } + \frac { 8 } { x + 3 }$

Question

Quizplus · Accepted Answer

The partial fraction decomposition of the given rational expression is $\frac { 3 } { x } + \frac { 3 } { x - 6 } + \frac { 8 } { x + 3 }$ after solving the equation by equating it to a general form of partial fractions and solving for the coefficients.

Write the Partial Fraction Decomposition of the Rational Expression 14x2−48x−54x(x−6)(x+3)\frac { 14 x ^ { 2 } - 48 x - 54 } { x ( x - 6 ) ( x + 3 ) }x(x−6)(x+3)14x2−48x−54​

Write the Partial Fraction Decomposition of the Rational Expression $\frac { 14 x ^ { 2 } - 48 x - 54 } { x ( x - 6 ) ( x + 3 ) }$