Rational Functions?

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1 Answer
Typo
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.

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