Write the partial fraction decomposition of the rational function. $\frac { 2 ( 4 x - 3 ) } { x ^ { 2 } - 9 }$
A) $\frac { 3 } { x - 3 } + \frac { 5 } { x - 3 }$
B) $\frac { 3 } { x - 3 } + \frac { 5 } { x + 3 }$
C) $\frac { 3 } { x - 3 } - \frac { 5 } { x - 3 }$.
D) $\frac { 3 } { x - 3 } + \frac { 2 } { x + 3 }$
E) $\frac { 3 } { x - 3 } - \frac { 5 } { x - 3 }$

Question

Write the partial fraction decomposition of the rational function.  $\frac { 2 ( 4 x - 3 ) } { x ^ { 2 } - 9 }$  
A) $\frac { 3 } { x - 3 } + \frac { 5 } { x - 3 }$
B) $\frac { 3 } { x - 3 } + \frac { 5 } { x + 3 }$
C) $\frac { 3 } { x - 3 } - \frac { 5 } { x - 3 }$.
D) $\frac { 3 } { x - 3 } + \frac { 2 } { x + 3 }$
E) $\frac { 3 } { x - 3 } - \frac { 5 } { x - 3 }$

Quizplus · Accepted Answer

The denominator can be factored as (x - 3)(x + 3), so the partial fraction decomposition is of the form:$\frac { 2 ( 4 x - 3 ) } { x ^ { 2 } - 9 } = \frac { A } { x - 3 } + \frac { B } { x + 3 }$Multiplying both sides by (x - 3)(x + 3), we get:$2 ( 4 x - 3 ) = A ( x + 3 ) + B ( x - 3 )$Setting x = 3, we get:$2 ( 4 ( 3 ) - 3 ) = A ( 3 + 3 ) + B ( 3 - 3 )$$2 ( 9 ) = 6 A$$A = 3$Setting x = -3, we get:$2 ( 4 ( -3 ) - 3 ) = A ( -3 + 3 ) + B ( -3 - 3 )$$2 ( -15 ) = -6 B$$B = 5$Therefore, the partial fraction decomposition is:$\frac { 2 ( 4 x - 3 ) } { x ^ { 2 } - 9 } = \frac { 3 } { x - 3 } + \frac { 5 } { x + 3 }$

Write the Partial Fraction Decomposition of the Rational Function 2(4x−3)x2−9\frac { 2 ( 4 x - 3 ) } { x ^ { 2 } - 9 }x2−92(4x−3)​

Write the Partial Fraction Decomposition of the Rational Function $\frac { 2 ( 4 x - 3 ) } { x ^ { 2 } - 9 }$