Write the partial fraction decomposition of the rational expression.
-$\frac { 5 x ^ { 3 } + 19 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$
A) $\frac { 5 x } { x ^ { 2 } + 3 } + \frac { 4 x + 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$
B) $\frac { 5 x } { x ^ { 2 } + 3 } + \frac { 4 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$
C) $\frac { 5 x + 1 } { x ^ { 2 } + 3 } + \frac { 4 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$
D) $\frac { 5 x } { x ^ { 2 } + 3 } + \frac { - 4 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$

Question

Quizplus · Accepted Answer

The correct partial fraction decomposition involves splitting the rational expression into terms with denominators $x^2 + 3$ and $(x^2 + 3)^2$. The coefficients are determined by equating and solving for the numerators.

Write the Partial Fraction Decomposition of the Rational Expression 5x3+19x−2(x2+3)2\frac { 5 x ^ { 3 } + 19 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }(x2+3)25x3+19x−2​

Write the Partial Fraction Decomposition of the Rational Expression $\frac { 5 x ^ { 3 } + 19 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$