Find Where Undefined/Discontinuous (6xyz)/(2xy-y)*(2x^2-7x+3)/(3xz-9z)

$\frac{6 x y z}{2 x y - y} \cdot \frac{2 x^{2} - 7 x + 3}{3 x z - 9 z}$

Step 1

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

$2 x y - y = 0$

Step 2

Solve for $x$ .

Add $y$ to both sides of the equation.

$2 x y = y$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $y$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Cancel the common factor of $y$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Set the denominator in $\frac{2 x^{2} - 7 x + 3}{3 x z - 9 z}$ equal to $0$ to find where the expression is undefined.

$3 x z - 9 z = 0$

Step 4

Solve for $x$ .

Add $9 z$ to both sides of the equation.

$3 x z = 9 z$

Divide each term in $3 x z = 9 z$ by $3 z$ and simplify.

Divide each term in $3 x z = 9 z$ by $3 z$ .

$\frac{3 x z}{3 z} = \frac{9 z}{3 z}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x z}{3 z} = \frac{9 z}{3 z}$

Rewrite the expression.

$\frac{x z}{z} = \frac{9 z}{3 z}$

Cancel the common factor of $z$ .

Cancel the common factor.

$\frac{x z}{z} = \frac{9 z}{3 z}$

Divide $x$ by $1$ .

$x = \frac{9 z}{3 z}$

Simplify the right side.

Cancel the common factor of $9$ and $3$ .

Factor $3$ out of $9 z$ .

$x = \frac{3 (3 z)}{3 z}$

Cancel the common factor.

$x = \frac{3 (3 z)}{3 z}$

Rewrite the expression.

$x = 3$

Step 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 $0$ .

$x = \frac{1}{2}, x = 3$

Step 6

Find Where Undefined/Discontinuous (6xyz)/(2xy-y)*(2x^2-7x+3)/(3xz-9z)

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