What is the domain of #f(x)=x/(x^2-5x)#?
The domain is every value that
So the only caveat we have here is that the denominator mustn't be 0. Or
We can solve this using the quadratic formula, sum and product, or, just do the easy thing and factor it out.
Since the product can't be zero, neither can, that is
So the domain D, is
Or that same thing in set notation.