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

Question

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

Quizplus · Accepted Answer

The denominator $x^2 + 5x + 4$ can be factored into $(x + 1)(x + 4)$. The partial fraction decomposition is then $\frac{A}{x + 1} + \frac{B}{x + 4}$. Solving for A and B gives $A = 1$ and $B = -1$, leading to the correct decomposition $\frac{1}{x + 1} - \frac{1}{x + 4}$.

Write the Partial Fraction Decomposition of the Rational Expression 3x2+5x+4\frac { 3 } { x ^ { 2 } + 5 x + 4 }x2+5x+43​

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