how do i find the domain of a rational function?

Question

tkhunny · Answer

Start with "All Real Numbers"
See if you must eliminate anything.

anonymous · Answer

Do i have to simplify?

tkhunny · Answer

Simplify what?  You must determine the Domain.  Simplifying MAY make it more obvious, but maybe not.

anonymous · Answer

So what do I do? My function is y=x^2+2x/x^2+2

tkhunny · Answer

No, it's not.  Use parentheses to clarify.  $y = \dfrac{x^{2}+2x}{x^{2}+2}$

Start with "All Real Numbers".
Must we remove anything?  Where can it go wrong?  What if the denominator is zero (0)?  Is that acceptable?

anonymous · Answer

No. I simplified and my teacher told me to then cancel but if i do that then x+2 cancels and so does x so i'm left with nothing.

tkhunny · Answer

There is no cancelling.  There is no simplification.  You can factor the Numerator if you like.  The ONLY question that is important is whether the Denominator can take on the value zero (0).  Can it?

anonymous · Answer

That's what I meant factoring. No it can't.

tkhunny · Answer

You're saying the Denominator cannot take on the value zero?  What does that mean for our Domain question?