f(x)=3x+1/x-5

Question

find the domain of the rational expression. 

Answer 1

Please use parentheses.  I assume you meant

 

f(x) = (3x + 1) / (x - 5)

 

The domain is all real numbers except where there is division by zero, which is at x = 5.  The domain is then all real numbers except 5.  You could express this as

 

(-∞, 5) U (5, ∞)