Rational function: How can you tell?

Question

I'm quite confused about the concept of rational functions. I understand that something like (x^1/2 +1)/(x+1) is a function, but how do you put that into p(x)/q(x)???

Also, a function with something like e^x in the denominator, is that rational? I don't feel like it is, but I may be wrong.

Answer 1

For you first example, p(x)=x^.5+1 and q(x)=(x+1).

Answer 2

(x^1/2 +1)/(x+1) isn't rational because it cannot be written as a ratio of polynomials (any attempt to make x^(1/2) into an integer power of x will cause the denominator to have noninteger powers of x). Something with e^x in it (unless this cancels upon simplification) is also not rational because e^x is not a polynomial.

Answer 3

A rational function is when one polynomial is divided by another polynomial. The exponents in the polynomials have to be whole numbers.

(x^(1/2) +1) is not a polynomial in this sense. Neither is e^x.