Answer
$(x+10)(x-10)^2$
Work Step by Step
We factor each denominator:
$$\begin{align*}
x^2-100&=(x-10)(x+10)\\
x^2-20x+100&=(x-10)^2.
\end{align*}$$
The Least Common Denominator (LCD) is the product of all factors in the two denominators, each taken once at the highest exponent:
$$(x+10)(x-10)^2.$$
