Question

Task: Nonpermissible Values for Rational Expressions [30 points] Write a rational expression that has the nonpermissible values x=0 and x=17. Explain your reasoning using complete sentences.

Answer 1

Answer:

A rational expression that has the nonpermissible values $x = 0$ and $x = 17$ is $f(x) = \frac{4}{x\cdot (x-17)}$.

Step-by-step explanation:

A rational expression has a nonpermissible value when for a given value of $x$, the denominator is equal to zero. In addition, we assume that both numerator and denominator are represented by polynomials, such that:

$f(x) = \frac{p(x)}{q(x)}$ (1)

Then, the factorized form of $q(x)$ must be:

$q(x) = x\cdot (x-17)$ (2)

If we know that $p(x) = 4$, then the rational expression is:

$f(x) = \frac{4}{x\cdot (x-17)}$ (3)

A rational expression that has the nonpermissible values $x = 0$ and $x = 17$ is $f(x) = \frac{4}{x\cdot (x-17)}$.