Rational Functions?

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1 Answer
Jun 25, 2018

Yes, it is a rational function. p(x)=x^3+9 and q(x)=9x.

Explanation:

f(x)=x^2/9+1/x
=x^2/9 *1 +1/x*1
=x^2/9 *x/x +1/x*9/9
=x^3/(9x)+9/(9x)
=(x^3+9)/(9x)

Let x^3+9=p(x) and 9x=q(x)
therefore f(x)=(p(x))/(q(x))

f(x) can be expressed in the form of a rational fraction therefore it is a rational function. p(x) matches the condition of having a leading coefficient of 1. p(x) and q(x) share no common factor.