feminizmiki

2022-01-17

Is the function in f(x)=x/29+2/x 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.

Donald Cheek

Beginner2022-01-18Added 41 answers

Step 1

Given function is,

$f\left(x\right)=\frac{x}{29}+\frac{2}{x}$

Step 2

Any function that can be written in the form,

$\frac{p\left(x\right)}{q\left(x\right)},q\left(x\right)\ne 0$ is called as rational function.

Step 3

Consider,

$f\left(x\right)=\frac{x}{29}+\frac{2}{x}$

Step 4

The LCM of the denominator is 29x.

$f\left(x\right)=\frac{{x}^{2}}{29x}+\frac{58}{29x}$

$f\left(x\right)=\frac{{x}^{2}+58}{29x}$

Step 5

Hence, the given function is rational.

$p\left(x\right)={x}^{2}+58$

q(x)=29x

Step 6

Where leading coefficient of p(x) is 1 and of q(x) is 29 and p(x) and q(x) has no common factors.

Given function is,

Step 2

Any function that can be written in the form,

Step 3

Consider,

Step 4

The LCM of the denominator is 29x.

Step 5

Hence, the given function is rational.

q(x)=29x

Step 6

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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