Find the Excluded Values (2x+12)/(2x^2+14x+12)

$\frac{2 x + 12}{2 x^{2} + 14 x + 12}$

Set the denominator in $\frac{2 x + 12}{2 x^{2} + 14 x + 12}$ equal to $0$ to find where the expression is undefined.

$2 x^{2} + 14 x + 12 = 0$

Solve for $x$ .

Factor the left side of the equation.

Factor $2$ out of $2 x^{2} + 14 x + 12$ .

Factor $2$ out of $2 x^{2}$ .

$2 (x^{2}) + 14 x + 12 = 0$

Factor $2$ out of $14 x$ .

$2 (x^{2}) + 2 (7 x) + 12 = 0$

Factor $2$ out of $12$ .

$2 x^{2} + 2 (7 x) + 2 \cdot 6 = 0$

Factor $2$ out of $2 x^{2} + 2 (7 x)$ .

$2 (x^{2} + 7 x) + 2 \cdot 6 = 0$

Factor $2$ out of $2 (x^{2} + 7 x) + 2 \cdot 6$ .

$2 (x^{2} + 7 x + 6) = 0$

Factor.

Factor $x^{2} + 7 x + 6$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $6$ and whose sum is $7$ .

$1, 6$

Write the factored form using these integers.

$2 ((x + 1) (x + 6)) = 0$

Remove unnecessary parentheses.

$2 (x + 1) (x + 6) = 0$

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

$x + 1 = 0$

$x + 6 = 0$

Set $x + 1$ equal to $0$ and solve for $x$ .

Set $x + 1$ equal to $0$ .

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

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.

$x = - 6$

The final solution is all the values that make $2 (x + 1) (x + 6) = 0$ true.

$x = - 1, - 6$

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 $0$ .

$x = - 6, x = - 1$

Find the Excluded Values (2x+12)/(2x^2+14x+12)

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