Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 1 } { x ^ { 2 } - 16 }$
A) $\frac { 1 } { 8 } \left( \frac { A } { x - 4 } - \frac { B } { x + 4 } \right)$
B) $\frac { 8 } { x - 4 } - \frac { 8 } { x + 4 }$
C) $\frac { 1 } { 8 } \left( \frac { 8 } { x - 4 } - \frac { 8 } { x + 4 } \right)$
D) $\frac { 1 } { 8 } \left( \frac { 1 } { x - 4 } - \frac { 1 } { x + 4 } \right)$
E) $\frac { 1 } { 8 } \left( \frac { 1 } { x - 4 } + \frac { 1 } { x + 4 } \right)$

Question

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ $\frac { 1 } { x ^ { 2 } - 16 }$ ​
A) $\frac { 1 } { 8 } \left( \frac { A } { x - 4 } - \frac { B } { x + 4 } \right)$
B) $\frac { 8 } { x - 4 } - \frac { 8 } { x + 4 }$
C) $\frac { 1 } { 8 } \left( \frac { 8 } { x - 4 } - \frac { 8 } { x + 4 } \right)$
D) $\frac { 1 } { 8 } \left( \frac { 1 } { x - 4 } - \frac { 1 } { x + 4 } \right)$
E) $\frac { 1 } { 8 } \left( \frac { 1 } { x - 4 } + \frac { 1 } { x + 4 } \right)$

Quizplus · Accepted Answer

The given expression can be factored as $\frac{1}{(x-4)(x+4)}$. The partial fraction decomposition of this expression is $\frac{1}{8}\left(\frac{1}{x-4} - \frac{1}{x+4}\right)$, which matches option D. This is because when you set up the partial fractions and solve for the constants, you find that each fraction must be multiplied by $\frac{1}{8}$ to equal the original expression when combined.

Write the Partial Fraction Decomposition of the Rational Expression 1x2−16\frac { 1 } { x ^ { 2 } - 16 }x2−161​

Write the Partial Fraction Decomposition of the Rational Expression $\frac { 1 } { x ^ { 2 } - 16 }$