Find Where Undefined/Discontinuous (y^2-15y-34)/(3y^2-12)

$\frac{y^{2} - 15 y - 34}{3 y^{2} - 12}$

Step 1

Set the denominator in $\frac{y^{2} - 15 y - 34}{3 y^{2} - 12}$ equal to $0$ to find where the expression is undefined.

$3 y^{2} - 12 = 0$

Step 2

Solve for $y$ .

Add $12$ to both sides of the equation.

$3 y^{2} = 12$

Divide each term in $3 y^{2} = 12$ by $3$ and simplify.

Divide each term in $3 y^{2} = 12$ by $3$ .

$\frac{3 y^{2}}{3} = \frac{12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y^{2}}{3} = \frac{12}{3}$

Divide $y^{2}$ by $1$ .

$y^{2} = \frac{12}{3}$

Simplify the right side.

Divide $12$ by $3$ .

$y^{2} = 4$

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

$y = \pm \sqrt{4}$

Simplify $\pm \sqrt{4}$ .

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

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

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

$y = \pm 2$

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.

$y = 2$

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

$y = - 2$

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

$y = 2, - 2$

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 $0$ .

$y = - 2, y = 2$

Step 4

Find Where Undefined/Discontinuous (y^2-15y-34)/(3y^2-12)

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