Find Where Undefined/Discontinuous x/(x(x-8))

$\frac{x}{x (x - 8)}$

Step 1

Set the denominator in $\frac{x}{x (x - 8)}$ equal to $0$ to find where the expression is undefined.

$x (x - 8) = 0$

Step 2

Solve for $x$ .

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x - 8 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x - 8$ equal to $0$ and solve for $x$ .

Set $x - 8$ equal to $0$ .

$x - 8 = 0$

Add $8$ to both sides of the equation.

$x = 8$

The final solution is all the values that make $x (x - 8) = 0$ true.

$x = 0, 8$

Step 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 $0$ .

$x = 0, x = 8$

Step 4

Find Where Undefined/Discontinuous x/(x(x-8))

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