Chapter 11, Problem 21PT

To determine

Write a rational expression for which 6 and 3 are excluded values.

Answer to Problem 21PT

In the expression $\frac{x^2+3x}{x-6}·\frac{1}{x-3}$ the excluded values $x\ne 6\text{and}x\ne 3$

Explanation of Solution

Given:

Write a rational expression for which 6 and 3 are excluded values.

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.

Multiply: $\frac{x^2+3x}{x-6}·\frac{1}{x-3}$; $x-6\ne 0\Rightarrow x\ne 6\text{and}x-3\ne 0\Rightarrow x\ne 3$

Thus, in the expression $\frac{x^2+3x}{x-6}·\frac{1}{x-3}$ the excluded values $x\ne 6\text{and}x\ne 3$