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

Question

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

Quizplus · Accepted Answer

The correct partial fraction decomposition of the given rational expression $\frac { 5 x ^ { 2 } + 3 x - 1 } { x ^ { 2 } ( x + 1 ) }$ is $\frac { 4 } { x } - \frac { 1 } { x ^ { 2 } } + \frac { 1 } { x + 1 }$. This is because when you decompose the given expression into partial fractions, you account for the factors in the denominator, which are $x^2$ and $x+1$, leading to terms that inversely relate to these factors.

Write the Partial Fraction Decomposition of the Rational Expression 5x2+3x−1x2(x+1)\frac { 5 x ^ { 2 } + 3 x - 1 } { x ^ { 2 } ( x + 1 ) }x2(x+1)5x2+3x−1​

Write the Partial Fraction Decomposition of the Rational Expression $\frac { 5 x ^ { 2 } + 3 x - 1 } { x ^ { 2 } ( x + 1 ) }$