For example, if you had:

x-3

------

5x+3

you'd only find the domain and use the denominator. Why wouldn't you also do the numerator?

And then you'd use both the numerator and the denominator in this:

(x^4-9x^2)^1/2

------------------------

x^2-4

WHY DO YOU USE BOTH OF THEM THERE? WHY NOT ON THE FIRST ONE?

~NEW QUESTION~

So if it was linear, like the first example, then you'd only have to use the denominator to find the domain because, mainly, your only concern is that the denominator may be 0, which then would make the value not real. But for the second example, you have
to use both the numerator and the denominator because they contain a root, and roots (if they're even) could make the situation imaginary thus not real. But what if the root in the denominator was a cube root?

For example

cube root (6x+3)

-----------------------

x^2-4

Would you need to use the numerator then?

For example

cube root (6x+3)

-----------------------

x^2-4

Would you need to use the numerator then?

## Comments

Yes.So if it was linear, like the first example, then you'd only have to usethe denominator to find the domain because, mainly, your only concern

is that the denominator may be 0, which then would make the value not

real.

Yes.But for the second example, you haveto use both the numerator and the denominator because they contain a

root, and roots (if they're even) could make the situation imaginary

thus not real. But what if the root in the denominator was a cube root?

Cube roots or any odd root can be any x value, so no need to use the numerator, then. If you have any other questions, just look at a graph, you will be able to see where the graph will not be continuous just focusing on the end points. Best of luck, ShannonComment