Decompose the fraction into partial fractions. $$\frac { 7 x ^ { 2 } + 6 x + 7 } { x ^ { 3 } + x }$$
A) $\frac { 7 } { x } - \frac { 6 } { x ^ { 2 } + 1 }$
B) $\frac { 6 } { x } - \frac { 7 } { x ^ { 2 } + 1 }$
C) $\frac { 7 } { x } + \frac { 6 } { x ^ { 2 } + 1 }$
D) $\frac { 6 } { x } + \frac { 7 } { x ^ { 2 } + 1 }$
E) none of these

Question

Quizplus · Accepted Answer

The denominator $x^3 + x$ can be factored as $x(x^2 + 1)$. The partial fraction decomposition should then involve terms over $x$ and $x^2 + 1$. The correct decomposition that matches the given polynomial in the numerator is $\frac{7}{x} + \frac{6}{x^2 + 1}$, making option C correct.

Decompose the Fraction into Partial Fractions 7x2+6x+7x3+x\frac { 7 x ^ { 2 } + 6 x + 7 } { x ^ { 3 } + x }x3+x7x2+6x+7​

Decompose the Fraction into Partial Fractions $\frac { 7 x ^ { 2 } + 6 x + 7 } { x ^ { 3 } + x }$