Is the function in f(x)=\frac{x}{29}+\frac{2}{x} a rational function?

Chardonnay Felix

Chardonnay Felix

Answered question

2021-09-11

Is the function in f(x)=x29+2x a rational function? If so, write it in the form p(x)q(x), the ratio of polynomials, where p(x) has leading coefficient 1, and p(x) and q(x) share no common factors.

Answer & Explanation

ensojadasH

ensojadasH

Skilled2021-09-12Added 100 answers

Given function is,
f(x)=x29+2x
Any function that can be written in the form,
p(x)q(x),q(x)0 is called as rational function.
Consider,
f(x)=x29+2x
The LCM of the denominator is 29x.
f(x)=x229x+5829x
f(x)=x2+5829x
Hence, the given function is rational.
p(x)=x2+58
q(x)=29x
Where leading coefficient of p(x) is 1 and of q(x) is 29 and p(x) and q(x) has no common factors.

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