#### Answer

$\frac{1}{\csc x-1}-\frac{1}{\csc x+1}$ can be simplified using $\left( \csc x-1 \right)\left( \csc x+1 \right)$ as the least common denominator.

#### Work Step by Step

In this case, the method of the least denominator must be used.
Thus, the denominator in the aforementioned case would be $\left( \csc x-1 \right)\left( \csc x+1 \right)$.