Find the Excluded Values (4xy^3)/(x^2y)*y/(8x)

$\frac{4 x y^{3}}{x^{2} y} \cdot \frac{y}{8 x}$

Step 1

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

$x^{2} y = 0$

Step 2

Solve for $x$ .

Divide each term in $x^{2} y = 0$ by $y$ and simplify.

Divide each term in $x^{2} y = 0$ by $y$ .

$\frac{x^{2} y}{y} = \frac{0}{y}$

Simplify the left side.

Cancel the common factor of $y$ .

Cancel the common factor.

$\frac{x^{2} y}{y} = \frac{0}{y}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{0}{y}$

Simplify the right side.

Divide $0$ by $y$ .

$x^{2} = 0$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Plus or minus $0$ is $0$ .

$x = 0$

Step 3

Set the denominator in $\frac{y}{8 x}$ equal to $0$ to find where the expression is undefined.

$8 x = 0$

Step 4

Divide each term in $8 x = 0$ by $8$ and simplify.

Divide each term in $8 x = 0$ by $8$ .

$\frac{8 x}{8} = \frac{0}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{0}{8}$

Divide $x$ by $1$ .

$x = \frac{0}{8}$

Simplify the right side.

Divide $0$ by $8$ .

$x = 0$

Step 5