Chapter 11, Problem 4PT

To determine

Identify the excluded value for each rational function $\frac{19+x}{x-5}$

Answer to Problem 4PT

Excluded value: $x-5\ne 0\Rightarrow x\ne 5$

Explanation of Solution

Given:

Identify the excluded value for each rational function $\frac{19+x}{x-5}$

Concept Used:

Rational expression is in the form $\frac{\text{P}}{\text{Q}}$ , where $\text{Q}\ne 0$ , denominator cannot be zero in any rational expression.

Excluded values are also called points of discontinuity. These are the values that make the denominator equal to zero and are not part of the domain.

In any rational function, the denominator cannot be zero.

To find the excluded value of the function, make denominator equal to zero and simplify.

Calculation:

In any rational function, the denominator cannot be zero.

To find the excluded value of the function, make denominator equal to zero and simplify.

The denominator $x-5$ cannot be zero.

Excluded value: $x-5\ne 0\Rightarrow x\ne 5$

Thus, excluded value: $x-5\ne 0\Rightarrow x\ne 5$