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

Question

Quizplus · Accepted Answer

The correct partial fraction decomposition is obtained by expressing the given rational expression in terms of its denominators. The numerator $x^2 + 3x - 2$ can be split such that part of it is over $x^2 + 2$ and another part over $(x^2 + 2)^2$, leading to the decomposition $\frac { 1 } { x ^ { 2 } + 2 } + \frac { 3 x - 4 } { \left( x ^ { 2 } + 2 \right) ^ { 2 } }$.

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

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