Chapter 11: Q7. (page 731)

Simplify each expression. State the excluded values of the variables.
$\frac{z - 6}{z^{2} - 3 z - 18}$

Short Answer

Expert verified

The given expression can be simplified to $\frac{1}{z + 3}$ . Excluded values of the variable are $6$ and localid="1648110564924" $- 3$ .

Step by step solution

Step 1. Factor.

Factor the given expression.

$\begin{matrix} \frac{(z - 6)}{z^{2} - 3 z - 18} = \frac{(z - 6)}{(z - 6) (z + 3)} \\ = \frac{1}{z + 3} \end{matrix}$

Step 2. Exclude the values.

Exclude the values for which $z^{2} - 3 z - 18$ equals 0.

$\begin{matrix} z^{2} - 3 z - 18 = 0 \\ (z - 6) (z + 3) = 0 \end{matrix}$

Step 3. Zero product property.

Apply zero product property to above equation.

$z - 6 = 0 or z + 3 = 0 z = 6 z = - 3$

Therefore, $z \neq 6$ and $z \neq - 3$ .

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Simplify each expression. State the excluded values of the variables.
$\frac{z - 6}{z^{2} - 3 z - 18}$

Short Answer

Step by step solution

Step 1. Factor.

Step 2. Exclude the values.

Step 3. Zero product property.

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Simplify each expression. State the excluded values of the variables.z−6z2−3z−18

Short Answer

Step by step solution

Step 1. Factor.

Step 2. Exclude the values.

Step 3. Zero product property.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Decision Maths

Applied Mathematics

Mechanics Maths

Theoretical and Mathematical Physics

Calculus

Study anywhere. Anytime. Across all devices.

Simplify each expression. State the excluded values of the variables.
$\frac{z - 6}{z^{2} - 3 z - 18}$