Find Where Undefined/Discontinuous ((z^2-81)/z)÷((z+9)/(z-9))

Set the denominator in ${\displaystyle \frac{z^2-81}{z}}$ equal to ${\displaystyle 0}$ to find where the expression is undefined.

Set the denominator in ${\displaystyle \frac{z+9}{z-9}}$ equal to ${\displaystyle 0}$ to find where the expression is undefined.

Add ${\displaystyle 9}$ to both sides of the equation.

Set the denominator in ${\displaystyle \frac{\frac{z^2-81}{z}}{\frac{z+9}{z-9}}}$ equal to ${\displaystyle 0}$ to find where the expression is undefined.

The equation is undefined where the denominator equals ${\displaystyle 0}$, the argument of a square root is less than ${\displaystyle 0}$, or the argument of a logarithm is less than or equal to ${\displaystyle 0}$.