Find Where Undefined/Discontinuous ((x-6)(x+3)(x+4))/((x+6)(x-3)(x-4))

$\frac{(x - 6) (x + 3) (x + 4)}{(x + 6) (x - 3) (x - 4)}$

Step 1

Set the denominator in $\frac{(x - 6) (x + 3) (x + 4)}{(x + 6) (x - 3) (x - 4)}$ equal to $0$ to find where the expression is undefined.

$(x + 6) (x - 3) (x - 4) = 0$

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 $0$ .

$x + 6 = 0$

$x - 3 = 0$

$x - 4 = 0$

Set $x + 6$ equal to $0$ and solve for $x$ .

Set $x + 6$ equal to $0$ .

$x + 6 = 0$

Subtract $6$ from both sides of the equation.

$x = - 6$

Set $x - 3$ equal to $0$ and solve for $x$ .

Set $x - 3$ equal to $0$ .

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

Set $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

The final solution is all the values that make $(x + 6) (x - 3) (x - 4) = 0$ true.

$x = - 6, 3, 4$

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 $0$ .

$x = - 6, x = 3, x = 4$

Step 4

Find Where Undefined/Discontinuous ((x-6)(x+3)(x+4))/((x+6)(x-3)(x-4))

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