Find Where Undefined/Discontinuous (t^2+2t-24)/(t^2-36)

$\frac{t^{2} + 2 t - 24}{t^{2} - 36}$

Step 1

Set the denominator in $\frac{t^{2} + 2 t - 24}{t^{2} - 36}$ equal to $0$ to find where the expression is undefined.

$t^{2} - 36 = 0$

Step 2

Solve for $t$ .

Add $36$ to both sides of the equation.

$t^{2} = 36$

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

$t = \pm \sqrt{36}$

Simplify $\pm \sqrt{36}$ .

Rewrite $36$ as $6^{2}$ .

$t = \pm \sqrt{6^{2}}$

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

$t = \pm 6$

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.

$t = 6$

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

$t = - 6$

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

$t = 6, - 6$

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 $0$ .

$t = - 6, t = 6$

Step 4

Find Where Undefined/Discontinuous (t^2+2t-24)/(t^2-36)

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