Rational Functions?

Question

Rational Functions?

1 Answer

Impact of this question

1463 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-25T15:08:06

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

Explanation:

$f (x) = \frac{x^{2}}{9} + \frac{1}{x}$ $f(x)=x^2/9+1/x$
$= \frac{x^{2}}{9} \cdot 1 + \frac{1}{x} \cdot 1$ $=x^2/9 *1 +1/x*1$
$= \frac{x^{2}}{9} \cdot \frac{x}{x} + \frac{1}{x} \cdot \frac{9}{9}$ $=x^2/9 *x/x +1/x*9/9$
$= \frac{x^{3}}{9 x} + \frac{9}{9 x}$ $=x^3/(9x)+9/(9x)$
$= \frac{x^{3} + 9}{9 x}$ $=(x^3+9)/(9x)$

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

$f(x)$ 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.

Science

Math

Humanities

... and beyond

Rational Functions?

1 Answer

Explanation:

Related questions

Impact of this question