Find the Excluded Values (-4x-32)/(x^2-12x+36)*(x^2-9x+18)/(3x+24)

$\frac{- 4 x - 32}{x^{2} - 12 x + 36} \cdot \frac{x^{2} - 9 x + 18}{3 x + 24}$

Set the denominator in $\frac{- 4 x - 32}{x^{2} - 12 x + 36}$ equal to $0$ to find where the expression is undefined.

$x^{2} - 12 x + 36 = 0$

Solve for $x$ .

Factor using the perfect square rule.

Rewrite $36$ as $6^{2}$ .

$x^{2} - 12 x + 6^{2} = 0$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$12 x = 2 \cdot x \cdot 6$

Rewrite the polynomial.

$x^{2} - 2 \cdot x \cdot 6 + 6^{2} = 0$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 6$ .

${(x - 6)}^{2} = 0$

Set the $x - 6$ equal to $0$ .

$x - 6 = 0$

Add $6$ to both sides of the equation.

$x = 6$

Set the denominator in $\frac{x^{2} - 9 x + 18}{3 x + 24}$ equal to $0$ to find where the expression is undefined.

$3 x + 24 = 0$

Solve for $x$ .

Subtract $24$ from both sides of the equation.

$3 x = - 24$

Divide each term in $3 x = - 24$ by $3$ and simplify.

Divide each term in $3 x = - 24$ by $3$ .

$\frac{3 x}{3} = \frac{- 24}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 24}{3}$

Divide $x$ by $1$ .

$x = \frac{- 24}{3}$

Simplify the right side.

Divide $- 24$ by $3$ .

$x = - 8$

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 $0$ .

$x = - 8, x = 6$

Find the Excluded Values (-4x-32)/(x^2-12x+36)*(x^2-9x+18)/(3x+24)

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