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

$\frac{2 x^{2}}{3 x^{2} - 4 x}$

Step 1

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

$3 x^{2} - 4 x = 0$

Step 2

Solve for $x$ .

Factor $x$ out of $3 x^{2} - 4 x$ .

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

$x (3 x) - 4 x = 0$

Factor $x$ out of $- 4 x$ .

$x (3 x) + x \cdot - 4 = 0$

Factor $x$ out of $x (3 x) + x \cdot - 4$ .

$x (3 x - 4) = 0$

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

$x = 0$

$3 x - 4 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $3 x - 4$ equal to $0$ and solve for $x$ .

Set $3 x - 4$ equal to $0$ .

$3 x - 4 = 0$

Solve $3 x - 4 = 0$ for $x$ .

Add $4$ to both sides of the equation.

$3 x = 4$

Divide each term in $3 x = 4$ by $3$ and simplify.

Divide each term in $3 x = 4$ by $3$ .

$\frac{3 x}{3} = \frac{4}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{4}{3}$

Divide $x$ by $1$ .

$x = \frac{4}{3}$

The final solution is all the values that make $x (3 x - 4) = 0$ true.

$x = 0, \frac{4}{3}$

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 $0$ .

$x = 0, x = \frac{4}{3}$

Step 4

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

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