Chapter 11, Problem 7PT

To determine

To simplify: the expression and state the Excluded value of the variables.

Answer to Problem 7PT

The simplified expression is $\frac{1}{z+3}$ and the excluded value is $-3,6$ .

Explanation of Solution

Given: $\frac{z-6}{z^2-3z-18}$

Calculation:

The objectives is to simplify the expression and state the excluded value of the variables.

The rational expression is simplified below.

  $\begin{array}{l}\frac{z-6}{z^2-3z-18}\\ =\frac{\left(z-6\right)}{\left(z-6\right)\left(z+3\right)}\\ =\frac{1}{z+3}\end{array}$

Therefore, the simplified expression is $\boxed{\frac{1}{z+3}}$ .

Exclude the values for which $z^2-3z-18=0$ .

So,

  $\begin{array}{l}{z}^2-3z-18=0\\ \left(z-6\right)\left(z+3\right)=0\\ z=-3,6\end{array}$

Therefore, the excluded value is $\boxed{-3,6}$ .

Conclusion:

Therefore, the simplified expression is $\frac{1}{z+3}$ and the excluded value is $-3,6$ .