If f(x) = (x+1)^-1 and g(x) = x-2, what is the domain of f(x) divided by g(x)

F(x)=(x+1)^-1

f(x)=1/(x+1)  so 

f(x)/g(x) is

1/[(x+1)(x-2)]

Since division by zero approaches infinity, it is not a real value, and is said to be undefined.  Division by zero is "not allowed", which just really means that it does not have a real value.  So in this case x cannot equal -1 or 2 so the domain is:

All real numbers except -1 or 2...which can be expressed as:

(-oo,-1),(-1,2),(2,+oo)