Rational Expressions

[nycmathguy]

College Algebra
Chapter 1/Section 7

The quotient of two polynomial functions is called a rational expression.

If f(x) and g(x) are polynomial functions, then
f(x)/g(x) is a rational expression. A rational expression is a fraction..

If f(x) = x/(x - 1), then f(x) is a rational expression in one variable.

If g(x) = (xy)^2/(x - y)^3, then g(x) is a rational expression in two variables.

Is any of this right?

Question

Is there such a thing as a rational expression in more than two variables? If so, can you give two examples?

Thank you.

 

[MathLover1]

you are confusing expressions with functions
f(x) = x/(x - 1), then f(x) is a rational function

x/(x - 1) is an expression

same for g(x)

a rational expression in more than two variables: (xyz^2)/(5x^2y^3z^-1)

 

[nycmathguy]

you are confusing expressions with functions
f(x) = x/(x - 1), then f(x) is a rational function

x/(x - 1) is an expression

same for g(x)

a rational expression in more than two variables: (xyz^2)/(5x^2y^3z^-1)

What am I confuses about? A rational expression is simply one polynomial divided by another. No?

 

[MathLover1]

yes, rational expression is simply one polynomial divided by another

but you say f(x) = x/(x - 1) is a rational expression, which is not; it is a rational function

 

[nycmathguy]

yes, rational expression is simply one polynomial divided by another

but you say f(x) = x/(x - 1) is a rational expression, which is not; it is a rational function

So, x/(x - 1) is a rational expression.

f(x) = x/(x - 1) is a rational function.

The difference is one contains f(x) = and the other does not.