Find the Excluded Values (9x^2)/(x-6)(x^2-36)/(3x-6)3/(4x^2+24x)

$\frac{9 x^{2}}{x - 6} \cdot \frac{x^{2} - 36}{3 x - 6} \cdot \frac{3}{4 x^{2} + 24 x}$

Set the denominator in $\frac{9 x^{2}}{x - 6}$ equal to $0$ to find where the expression is undefined.

$x - 6 = 0$

Add $6$ to both sides of the equation.

$x = 6$

Set the denominator in $\frac{x^{2} - 36}{3 x - 6}$ equal to $0$ to find where the expression is undefined.

$3 x - 6 = 0$

Solve for $x$ .

Add $6$ to both sides of the equation.

$3 x = 6$

Divide each term in $3 x = 6$ by $3$ and simplify.

Divide each term in $3 x = 6$ by $3$ .

$\frac{3 x}{3} = \frac{6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{6}{3}$

Divide $x$ by $1$ .

$x = \frac{6}{3}$

Simplify the right side.

Divide $6$ by $3$ .

$x = 2$

Set the denominator in $\frac{3}{4 x^{2} + 24 x}$ equal to $0$ to find where the expression is undefined.

$4 x^{2} + 24 x = 0$

Solve for $x$ .

Factor $4 x$ out of $4 x^{2} + 24 x$ .

Factor $4 x$ out of $4 x^{2}$ .

$4 x (x) + 24 x = 0$

Factor $4 x$ out of $24 x$ .

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

Factor $4 x$ out of $4 x (x) + 4 x (6)$ .

$4 x (x + 6) = 0$

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

$x = 0$

$x + 6 = 0$

Set $x$ equal to $0$ .

$x = 0$

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.

$x = - 6$

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

$x = 0, - 6$

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 $0$ .

$x = - 6, x = 0, x = 2, x = 6$

Find the Excluded Values (9x^2)/(x-6)*(x^2-36)/(3x-6)*3/(4x^2+24x)

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Find the Excluded Values (9x^2)/(x-6)(x^2-36)/(3x-6)3/(4x^2+24x)