Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 4 x ^ { 2 } + 3 x + 20 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$
A) $\frac { 4 } { x ^ { 2 } + 5 } + \frac { 3 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$
B) $\frac { 4 x + 20 } { x ^ { 2 } + 5 } + \frac { 3 x } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$
C) $\frac { 3 x + 4 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$
D) $\frac { 4 } { x ^ { 2 } + 5 } - \frac { 3 x } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$
E) $\frac { 4 } { x ^ { 2 } + 5 } + \frac { 3 x } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$

Question

Write the partial fraction decomposition of the rational expression.Check your result algebraically.  $\frac { 4 x ^ { 2 } + 3 x + 20 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$  
A) $\frac { 4 } { x ^ { 2 } + 5 } + \frac { 3 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$
B) $\frac { 4 x + 20 } { x ^ { 2 } + 5 } + \frac { 3 x } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$
C) $\frac { 3 x + 4 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$
D) $\frac { 4 } { x ^ { 2 } + 5 } - \frac { 3 x } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$
E) $\frac { 4 } { x ^ { 2 } + 5 } + \frac { 3 x } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$

Quizplus · Accepted Answer

The correct partial fraction decomposition of the given rational expression $\frac { 4 x ^ { 2 } + 3 x + 20 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$ is $\frac { 4 } { x ^ { 2 } + 5 } + \frac { 3 x } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$. This is because the numerator can be split into a linear combination that matches the denominators' degrees and repetition.

Write the Partial Fraction Decomposition of the Rational Expression 4x2+3x+20(x2+5)2\frac { 4 x ^ { 2 } + 3 x + 20 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }(x2+5)24x2+3x+20​

Write the Partial Fraction Decomposition of the Rational Expression $\frac { 4 x ^ { 2 } + 3 x + 20 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$