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

A rational expression that has the nonpermissible values
`x = 0` and
`x = 17` is
`f(x) = (4)/(x\cdot (x-17))`.

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) = (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) = (4)/(x\cdot (x-17))` (3)

A rational expression that has the nonpermissible values
`x = 0` and
`x = 17` is
`f(x) = (4)/(x\cdot (x-17))`.