I have a rational function: $y = \frac{x^2 - 3x}{x^2 + 2x - 48}$
The explanation I was given to find the x-intercepts was: "let y = 0, and solve for x. Basically you just set the numerator of the fraction equal to 0 and factor."
What does "basically" mean? Is this always the case? Do you simply set the numerator expression equal to zero, and always ignore the contents of the denominator? If so, why do you ignore the contents of the denominator?
You can't just ignore the denominator. After following the suggested procedure, you have to check whether the point you found is also a zero of the denominator. If so, $y$ is not defined at the point in question.
$x$ has no chance of being a zero unless it's a zero of the numerator, but that's not the whole story.