"A rational function is defined as the quotient of polynomials in which the denominator has a degree of at least 1"If we are talking merely about x, then I get the concept. A rational function f(x) could be written as "p(x)q(x), where q(x)≠0."The issue that I'm having is that of talking about rational functions of n variables. For instance, what would be the meaning of 'f(x,y) is a rational function of x &amp; y′?

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&quot;A rational function is defined as the quotient of polynomials in which the denominator has a degree of at least 1&quot;If we are talking merely about x, then I get the concept. A rational function f(x) could be written as &quot;p(x)q(x), where q(x)≠0.&quot;The issue that I&#039;m having is that of talking about rational functions of n variables. For instance, what would be the meaning of &#039;f(x,y) is a rational function of x &amp;amp; y′?

vefibiongedogn7z · Accepted Answer

The definition applies to n variables as well. For any two polynomials p,q, the function f(x1,x2,…xn)=p(x1,x2,…xn)q(x1,x2,…xn) is a rational function (if q is not constant).    For example, f(x,y)=xy is a rational function of 2 variables.

Elodie Williamson · Accepted Answer

For instance, f(x,y)=p(x,y)q(x,y) is a rational function of x and y if p and q are polynomials in x and y... So p and q are finite sums of terms of the form axnym, where a is a numerical coefficient and n and m are whole numbers... and, of course, the degree of q is 1 or more...

"A rational function is defined as the quotient of polynomials in which the denominator has a degree

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