The domain of a rational function is all of the x-values that don't break the function. If a value of x doesn't make the denominator zero, it's part of the domain. If a value of x makes the function blow up, it's not part of the domain. These x-values become asymptotes. Sure, the first rule of rational functions is "we don't talk about rational functions," but the second rule is to never divide by zero. Don't do it. The rule breakers get kicked out of the domain. Ka-pow.
Sample Problem
What's the domain of the following function?
The domain is everywhere the denominator isn't zero.
Here, the denominator will only be zero when x = 0.
So, our domain is -∞ < x < ∞, except x = 0. We can also write that as x ≠ 0.
Sample Problem
What's the domain of 
?
For the domain, everything that doesn't make the denominator zero is fair game. This time, plugging in x = 1 will give us an undefined fraction, so our domain is -∞ < x < ∞, except x = 1. In other words, x ≠ 1.
Sample Problem
What's the domain of 
?
Same old, same old. The domain is everywhere the denominator isn't zero. We'll get a zero in our denominator when x = 1 or x = 2. That tells us we've got a domain of -∞ < x < ∞, except x = 1 and x = 2. Or, to keep it short and sweet, the domain is x ≠ 1 and x ≠ 2.