Algebra Examples

$\frac{y^{2} - 36}{y} \div \frac{y + 6}{y - 6}$

Step 1

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

$y = 0$

Step 2

Set the denominator in $\frac{y + 6}{y - 6}$ equal to $0$ to find where the expression is undefined.

$y - 6 = 0$

Step 3

Add $6$ to both sides of the equation.

$y = 6$

Step 4

Set the denominator in $\frac{y^{2} - 36}{y} \div \frac{y + 6}{y - 6}$ equal to $0$ to find where the expression is undefined.

$\frac{y + 6}{y - 6} = 0$

Step 5

Solve for $y$ .

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Step 5.1

Set the numerator equal to zero.

$y + 6 = 0$

Step 5.2

Subtract $6$ from both sides of the equation.

$y = - 6$

Step 6

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 $0$ .

$y = - 6, y = 0, y = 6$

Step 7