we have
f(x)=4x+5
g(x)=x-1
so
f/g=f(x)/g(x)=(4x+5)/(x-1)
Remember that
In a quotient, the denominator can not be equal to zero
so
In this problem
the value of x can not be equal to 1, because the function does not exist
therefore
the domain is all real numbers except for x=1
in notation interval is
(-infinite,1) U (1, infinite)