Write the partial fraction decomposition of the rational expression.
$\frac { 1 } { 100 x ^ { 2 } - 81 }$
A) $\frac { 1 } { 18 } \left( \frac { x - 10 } { 10 x - 9 } - \frac { x - 10 } { 10 x + 9 } \right)$
B) $\frac { 1 } { 100 x ^ { 2 } } - \frac { 1 } { 81 }$
C) $\frac { 1 } { 18 } \left( \frac { 1 } { 10 x - 9 } - \frac { 1 } { 10 x + 9 } \right)$
D) $\frac { 1 } { 9 } \left( \frac { 1 } { 10 x + 9 } - \frac { 1 } { 10 x - 9 } \right)$
E) $\frac { 1 } { 9 } \left( \frac { 1 } { 10 x - 9 } - \frac { 1 } { 10 x + 9 } \right)$

Question

Quizplus · Accepted Answer

The denominator can be factored as a difference of squares: $100x^2 - 81 = (10x)^2 - 9^2 = (10x - 9)(10x + 9)$. The partial fraction decomposition involves breaking this into two fractions with denominators $10x - 9$ and $10x + 9$, respectively, which matches option C.

Write the Partial Fraction Decomposition of the Rational Expression 1100x2−81\frac { 1 } { 100 x ^ { 2 } - 81 }100x2−811​

Write the Partial Fraction Decomposition of the Rational Expression $\frac { 1 } { 100 x ^ { 2 } - 81 }$