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

$\frac{3 x}{x (2 x - 3)}$

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

$x (2 x - 3) = 0$

Solve for $x$ .

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

$x = 0$

$2 x - 3 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $2 x - 3$ equal to $0$ and solve for $x$ .

Set $2 x - 3$ equal to $0$ .

$2 x - 3 = 0$

Solve $2 x - 3 = 0$ for $x$ .

Add $3$ to both sides of the equation.

$2 x = 3$

Divide each term in $2 x = 3$ by $2$ and simplify.

Divide each term in $2 x = 3$ by $2$ .

$\frac{2 x}{2} = \frac{3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{3}{2}$

Divide $x$ by $1$ .

$x = \frac{3}{2}$

The final solution is all the values that make $x (2 x - 3) = 0$ true.

$x = 0, \frac{3}{2}$

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 $0$ .

$x = 0, x = \frac{3}{2}$

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

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