Write the partial fraction decomposition of the rational expression. $\frac { 1 } { 16 x ^ { 2 } - 121 }$
A) $\frac { 1 } { 22 } \left( \frac { 1 } { 4 x - 11 } - \frac { 1 } { 4 x + 11 } \right)$
B) $\frac { 1 } { 11 } \left( \frac { 1 } { 4 x - 11 } - \frac { 1 } { 4 x + 11 } \right)$
C) $\frac { 1 } { 4 x ^ { 2 } } - \frac { 1 } { 121 }$
D) $\frac { 1 } { 22 } \left( \frac { x - 4 } { 4 x - 11 } - \frac { x - 4 } { 4 x + 11 } \right)$
E) $\frac { 1 } { 11 } \left( \frac { 1 } { 4 x + 11 } - \frac { 1 } { 4 x - 11 } \right)$

Question

Quizplus · Accepted Answer

The denominator can be factored as $(4x)^2 - 11^2$, which is a difference of squares and equals $(4x - 11)(4x + 11)$. The correct partial fraction decomposition is $\frac{1}{22}\left(\frac{1}{4x-11} - \frac{1}{4x+11}\right)$, matching choice A.

Write the Partial Fraction Decomposition of the Rational Expression 116x2−121\frac { 1 } { 16 x ^ { 2 } - 121 }16x2−1211​

Write the Partial Fraction Decomposition of the Rational Expression $\frac { 1 } { 16 x ^ { 2 } - 121 }$