Answer
$(x - 6)(x - 6)(x + 1)$ or $(x - 6)^2(x + 1)$
Work Step by Step
To find the least common denominator (LCD) of the two rational expressions, completely factor the denominators first:
First expression:
$\dfrac{1}{(x - 6)(x + 1)}$
Second expression:
$\dfrac{1}{(x - 6)(x - 6)}$
The LCD incorporates all factors in the denominators of both rational expressions, where a common factor will be used the maximum number of times it appears as a factor of the polynomial.
In this case, $x-6$ has to be used twice.
Therefore, the LCD for these two rational expressions is:
$(x - 6)(x - 6)(x + 1)$ or $(x - 6)^2(x + 1)$
