Simplify the function , and determine its domain.
Before simplifying the function, we note that is not defined when either of the fractions has a denominator of 0.
is not defined when either or .
So, the domain of is
To simplify the function, we must subtract the algebraic fractions. To do this, we must find a common denominator for the fractions.
The common denominator is the product of the denominators:
So in its simplest form,
which may be written as
Therefore, the domain of is .