Write the partial fraction decomposition of the rational expression.
$$\frac { 5 } { x ^ { 2 } + 10 x + 16 }$$
A) $\frac { 5 } { 6 } \left( \frac { 1 } { x - 2 } - \frac { 1 } { x - 8 } \right)$
B) $\frac { 5 } { 6 } \left( \frac { 1 } { x + 2 } - \frac { 1 } { x + 8 } \right)$
C) $\frac { 5 } { 6 } \left( \frac { 1 } { x + 8 } - \frac { 1 } { x + 2 } \right)$
D) $\frac { 5 } { x ^ { 2 } } + \frac { 1 } { 2 x } + \frac { 5 } { 16 }$
E) $\frac { 5 } { x ^ { 2 } + 10 x + 16 }$

Question

Quizplus · Accepted Answer

The denominator $x^2 + 10x + 16$ can be factored as $(x + 2)(x + 8)$. The correct partial fraction decomposition must involve these factors in the denominators, which matches option B.

Write the Partial Fraction Decomposition of the Rational Expression 5x2+10x+16\frac { 5 } { x ^ { 2 } + 10 x + 16 }x2+10x+165​

Write the Partial Fraction Decomposition of the Rational Expression $\frac { 5 } { x ^ { 2 } + 10 x + 16 }$