Find Where Undefined/Discontinuous (6x)/(12x^2-6x)

$\frac{6 x}{12 x^{2} - 6 x}$

Step 1

Set the denominator in $\frac{6 x}{12 x^{2} - 6 x}$ equal to $0$ to find where the expression is undefined.

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

Step 2

Solve for $x$ .

Factor $6 x$ out of $12 x^{2} - 6 x$ .

Factor $6 x$ out of $12 x^{2}$ .

$6 x (2 x) - 6 x = 0$

Factor $6 x$ out of $- 6 x$ .

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

Factor $6 x$ out of $6 x (2 x) + 6 x (- 1)$ .

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

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

$x = 0$

$2 x - 1 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $2 x - 1$ equal to $0$ and solve for $x$ .

Set $2 x - 1$ equal to $0$ .

$2 x - 1 = 0$

Solve $2 x - 1 = 0$ for $x$ .

Add $1$ to both sides of the equation.

$2 x = 1$

Divide each term in $2 x = 1$ by $2$ and simplify.

Divide each term in $2 x = 1$ by $2$ .

$\frac{2 x}{2} = \frac{1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{1}{2}$

Divide $x$ by $1$ .

$x = \frac{1}{2}$

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

$x = 0, \frac{1}{2}$

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 $0$ .

$x = 0, x = \frac{1}{2}$

Step 4

Find Where Undefined/Discontinuous (6x)/(12x^2-6x)

Related Questions

Support LCMGCF.com by disabling your adblocker.