Find Where Undefined/Discontinuous (t^2+4t-12)/(t^2-4)

$\frac{t^{2} + 4 t - 12}{t^{2} - 4}$

Step 1

Set the denominator in $\frac{t^{2} + 4 t - 12}{t^{2} - 4}$ equal to $0$ to find where the expression is undefined.

$t^{2} - 4 = 0$

Step 2

Solve for $t$ .

Add $4$ to both sides of the equation.

$t^{2} = 4$

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

$t = \pm \sqrt{4}$

Simplify $\pm \sqrt{4}$ .

Rewrite $4$ as $2^{2}$ .

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

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

$t = \pm 2$

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.

$t = 2$

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

$t = - 2$

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

$t = 2, - 2$

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 $0$ .

$t = - 2, t = 2$

Step 4

Find Where Undefined/Discontinuous (t^2+4t-12)/(t^2-4)

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