I have this function where I need to find the $x$-intercepts
I see they are $x = 0, 4$. And know that this is found by doing: $x=0, (x-4) = 0$ [Solve].
But why is this only done for the numerator?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.Sign up to join this community
If you're asking why we set only the numerator equal to 0 and not the denominator, recall that $0$ divided by any nonzero number is $0$. Similarly, any number divided by $0$ is undefined.
Therefore in your case, the fraction is only equal to $0$ when its numerator is equal to $0$ and it's denominator is not equal to $0$, as having a denominator equal to $0$ (which is akin to dividing by $0$) would render the expression undefined.