Question

How do I create a rational function?

Answer 1

Can you make a polynomial?

Answer 2

yes

Answer 3

Well, a rational function is simply a fraction, with a polynomial numerator and a polynomial denominator.
Case closed :)

Answer 4

In fact, polynomials themselves are rational functions.

Answer 5

oh, and all that I need to do to create one is to create 2 polynomials, one for the numerator, and one for the denominator, right?

Answer 6

Yeah... but of course, let's make it interesting, don't make it, say
\[\huge \frac{x^2-4}{(x-2)(x+2)}\]which is just equal to 1.
Use polynomials that don't cancel out...
Although, understandably, since constants are also polynomials, they are also rational functions... boring ones, though.

Answer 7

Polynomials are to Rational functions as
Integers are to Rational numbers. See what I did there? ;)

Answer 8

So it should be one that cannot be cancelled out, only simplified, right? Now I think I get it, I just need to make one that works.

Answer 9

Not that it SHOULD.
Constants are also polynomials.
Polynomials are also rational functions, but maybe you ought to illustrate a little more creativity, and less trivialness when constructing these rational functions :D

Answer 10

So, \[\frac{ x^2-6x-72 }{ y^2+7y-98 }\] is a rational function, right?

Answer 11

Yes...

Answer 12

Of two variables, though.

Answer 13

Should it be only one variable?

Answer 14

Not really

Answer 15

Okay, thanks!