Find Where Undefined/Discontinuous y=((x+6)(x+2)(x+8))/((x+9)(x+7))

$y = \frac{(x + 6) (x + 2) (x + 8)}{(x + 9) (x + 7)}$

Step 1

Set the denominator in $\frac{(x + 6) (x + 2) (x + 8)}{(x + 9) (x + 7)}$ equal to $0$ to find where the expression is undefined.

$(x + 9) (x + 7) = 0$

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 $0$ .

$x + 9 = 0$

$x + 7 = 0$

Set $x + 9$ equal to $0$ and solve for $x$ .

Set $x + 9$ equal to $0$ .

$x + 9 = 0$

Subtract $9$ from both sides of the equation.

$x = - 9$

Set $x + 7$ equal to $0$ and solve for $x$ .

Set $x + 7$ equal to $0$ .

$x + 7 = 0$

Subtract $7$ from both sides of the equation.

$x = - 7$

The final solution is all the values that make $(x + 9) (x + 7) = 0$ true.

$x = - 9, - 7$

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 $0$ .

$x = - 9, x = - 7$

Step 4

Find Where Undefined/Discontinuous y=((x+6)(x+2)(x+8))/((x+9)(x+7))

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