#### Answer

$(x+9)^{2}(x-9)$

#### Work Step by Step

We are given the denominators $x^{2}-81$ and $x^{2}+18x+81$.
In order to find the least common denominator, we must factor each denominator.
$x^{2}-81=(x+9)(x-9)$
$x^{2}+18x+81=(x+9)(x+9)=(x+9)^{2}$
Next, we multiply together all distinct factors from each denominator, with each factor raised to the greatest power that occurs in any denominator.
$LCD=(x+9)^{2}\times(x-9)=(x+9)^{2}(x-9)$