Chapter 9.1, Problem 2CYP

To determine

Find the undefined value of $x$ .

Answer to Problem 2CYP

The correct option is $G$ .

Explanation of Solution

Given information: Given expression is $\frac{x\left(x^2+8x+12\right)}{-6\left(x^2-3x-10\right)}$

Calculation:

Factor the denominator to obtain:

  $\begin{array}{l}=\frac{x\left(x^2+8x+12\right)}{-6\left(x^2-5x+2x-10\right)}\\ =\frac{x\left(x^2+8x+12\right)}{-6\left(x\left(x-5\right)+2\left(x-5\right)\right)}\\ =\frac{x\left(x^2+8x+12\right)}{-6\left(\left(x-5\right)\left(x+2\right)\right)}\end{array}$

The given expression is undefined when its denominator is equal to zero.

  $\begin{array}{l}\left(x-5\right)\left(x+2\right)=0\\ x-5=0\text{ or }x+2=0\\ x=5\text{ or }x=-2\end{array}$

Note that the denominator of the given expression will be equal to zero when $x=-2$ or and $x=5$

Thus, the correct option is $G$ .