Chapter 11.5, Problem 4STP

For Exercises 1-4, choose the correct letter.

What is the excluded value of the rational expression? include all possible solutions.

$\frac{1}{x^2+2x-24}$

F. 0.24

G. 6, 4

H. 4, 6

I. 4, -6

To determine

To choose the correct answer.

Answer to Problem 4STP

I) $4,-6$

Explanation of Solution

Given information:

What is the excluded value of the rational expression? Include all possible solutions.

  $\frac{1}{x^2+2x-24}$

F) $0,24$

G) $6,-4$

H) $4,6$

I) $4,-6$

Calculation:

Calculate the value of $x$ for which the value of $x^2+2x-24=0$ :

  $\begin{array}{l}{x}^2+2x-24=0\\ x^2+6x-4x-24=0\\ x\left(x+6\right)-4\left(x+6\right)=0\\ \left(x+6\right)\left(x-4\right)=0\\ x=4,-6\end{array}$

Hence, the correct option is $x=4,-6$ .