Why aren't rational expressions with square roots in the numerator rational?

[Sparky_]

Homework Statement

I have volunteered to help a friend's son with his Algebra 2 (thinking - no problem, I've had Calc 1-3, differential equation, complex variables, probability / stats and so on.

So I start to help and the first questions:

Why aren't these rational expressions:
$$\frac {\sqrt(x)}{(x+3)}$$

and


$$\frac {\sqrt{(x-y)^2}}{(x)}$$

Homework Equations

The Attempt at a Solution

I know if the square root wasn't in the numerator they would be rational - at least I hope I'm correct.

I don't know why they aren't reational.

Thanks
-Sparky

 

[HallsofIvy]

Yes, a "rational function" is defined as "a polynomial divided by a polynomial". What you give is not a rational function because $\sqrt{x}$ is not a polynomial.

 

[Sparky_]

Ok - "polynomial divided by polynomial"

I was going to have to dig out my old algebra book. - in fact I probably still will have to dig it out to avoid embarassment.

Thanks so much!