Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the
constants.
-$$\frac { 5 x - 3 } { ( x - 5 ) \left( x ^ { 2 } + x + 5 \right) }$$
A) $\frac { A } { x - 5 } + \frac { B } { x ^ { 2 } + x + 5 } + \frac { C } { ( x - 5 ) \left( x ^ { 2 } + x + 5 \right) }$
B) $\frac { \mathrm { A } } { \mathrm { x } - 5 } + \frac { \mathrm { B } } { \mathrm { x } ^ { 2 } + \mathrm { x } + 5 }$
C) $\frac { A } { x - 5 } + \frac { B x + C } { x ^ { 2 } + x + 5 } + \frac { D } { ( x - 5 ) \left( x ^ { 2 } + x + 5 \right) }$
D) $\frac { A } { x - 5 } + \frac { B x + C } { x ^ { 2 } + x + 5 }$

Question

Quizplus · Accepted Answer

For a linear factor, you use a single constant in the numerator (A for the (x-5) term). For a quadratic factor that cannot be factored further, you use a linear expression in the numerator (Bx + C for the $x^2 + x + 5$ term).

Write the Form of the Partial Fraction Decomposition of the Rational