Find the least common denominator.
-$\frac { 5 } { x ^ { 2 } - 81 } + \frac { 4 } { x ( x - 9 ) }$
A)x(x + 9)
B)x(x - 9)
C) $\left( x ^ { 2 } + 9 \right) \left( x ^ { 2 } - 9 \right)$
D)x(x + 9)(x - 9)

Question

Quizplus · Accepted Answer

The least common denominator (LCD) must account for all factors present in the denominators of the given fractions. The first denominator is $x^2 - 81$, which factors into $(x + 9)(x - 9)$ using the difference of squares formula. The second denominator is already factored as $x(x - 9)$. The LCD must include each unique factor, so it is $x(x + 9)(x - 9)$, making option D correct.

Find the Least Common Denominator 5x2−81+4x(x−9)\frac { 5 } { x ^ { 2 } - 81 } + \frac { 4 } { x ( x - 9 ) }x2−815​+x(x−9)4​

Find the Least Common Denominator $\frac { 5 } { x ^ { 2 } - 81 } + \frac { 4 } { x ( x - 9 ) }$