Find Where Undefined/Discontinuous (y-3)/(y^2-9)

$\frac{y - 3}{y^{2} - 9}$

Set the denominator in $\frac{y - 3}{y^{2} - 9}$ equal to $0$ to find where the expression is undefined.

$y^{2} - 9 = 0$

Solve for $y$ .

Add $9$ to both sides of the equation.

$y^{2} = 9$

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

$y = \pm \sqrt{9}$

Simplify $\pm \sqrt{9}$ .

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

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

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

$y = \pm 3$

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.

$y = 3$

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

$y = - 3$

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

$y = 3, - 3$

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 $0$ .

$y = - 3, y = 3$

Find Where Undefined/Discontinuous (y-3)/(y^2-9)

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