Find Where Undefined/Discontinuous ((x^2-16)/x)÷((x+4)/(x-4))

Set the denominator in ${\displaystyle \frac{x^2-16}{x}}$ equal to ${\displaystyle 0}$ to find where the expression is undefined.

Set the denominator in ${\displaystyle \frac{x+4}{x-4}}$ equal to ${\displaystyle 0}$ to find where the expression is undefined.

Add ${\displaystyle 4}$ to both sides of the equation.

Set the denominator in ${\displaystyle \frac{\frac{x^2-16}{x}}{\frac{x+4}{x-4}}}$ 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 ${\displaystyle 0}$.