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

Question

Quizplus · Accepted Answer

The given expression $\frac{3}{x^2(x^2+2)}$ can be decomposed into partial fractions where each term in the denominator is considered separately. The correct decomposition balances the original fraction, and option D correctly splits the fraction into two parts, each with a coefficient that when combined, equals the original fraction.

Find the Partial Fraction Decomposition for the Rational Expression 3x2(x2+2)\frac { 3 } { x ^ { 2 } \left( x ^ { 2 } + 2 \right) }x2(x2+2)3​

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