Find Where Undefined/Discontinuous ((z^2-49)/z)÷((z+7)/(z-7))

Set the denominator in ${\displaystyle \frac{z^2-49}{z}}$ equal to ${\displaystyle 0}$ to find where the expression is undefined.

Set the denominator in ${\displaystyle \frac{z+7}{z-7}}$ equal to ${\displaystyle 0}$ to find where the expression is undefined.

Add ${\displaystyle 7}$ to both sides of the equation.

Set the denominator in ${\displaystyle \frac{\frac{z^2-49}{z}}{\frac{z+7}{z-7}}}$ 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 ${\displaystyle 0}$.