Find Where Undefined/Discontinuous (z^2+8z+15)/(z^2-9)

$\frac{z^{2} + 8 z + 15}{z^{2} - 9}$

Step 1

Set the denominator in $\frac{z^{2} + 8 z + 15}{z^{2} - 9}$ equal to $0$ to find where the expression is undefined.

$z^{2} - 9 = 0$

Step 2

Solve for $z$ .

Add $9$ to both sides of the equation.

$z^{2} = 9$

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$z = \pm \sqrt{9}$

Simplify $\pm \sqrt{9}$ .

Rewrite $9$ as $3^{2}$ .

$z = \pm \sqrt{3^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$z = \pm 3$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$z = 3$

Next, use the negative value of the $\pm$ to find the second solution.

$z = - 3$

The complete solution is the result of both the positive and negative portions of the solution.

$z = 3, - 3$

Step 3

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$z = - 3, z = 3$

Step 4

Find Where Undefined/Discontinuous (z^2+8z+15)/(z^2-9)

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