Find the Excluded Values (4x^2-12x)/(3x^2+15x)

$\frac{4 x^{2} - 12 x}{3 x^{2} + 15 x}$

Set the denominator in $\frac{4 x^{2} - 12 x}{3 x^{2} + 15 x}$ equal to $0$ to find where the expression is undefined.

$3 x^{2} + 15 x = 0$

Solve for $x$ .

Factor $3 x$ out of $3 x^{2} + 15 x$ .

Factor $3 x$ out of $3 x^{2}$ .

$3 x (x) + 15 x = 0$

Factor $3 x$ out of $15 x$ .

$3 x (x) + 3 x (5) = 0$

Factor $3 x$ out of $3 x (x) + 3 x (5)$ .

$3 x (x + 5) = 0$

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

$x = 0$

$x + 5 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x + 5$ equal to $0$ and solve for $x$ .

Set $x + 5$ equal to $0$ .

$x + 5 = 0$

Subtract $5$ from both sides of the equation.

$x = - 5$

The final solution is all the values that make $3 x (x + 5) = 0$ true.

$x = 0, - 5$

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 $0$ .

$x = - 5, x = 0$

Find the Excluded Values (4x^2-12x)/(3x^2+15x)

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