Algebra Examples

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

Step 1

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

$- 4 y = 0$

Step 2

Divide each term in $- 4 y = 0$ by $- 4$ and simplify.

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Step 2.1

Divide each term in $- 4 y = 0$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{0}{- 4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{0}{- 4}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{0}{- 4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $0$ by $- 4$ .

$y = 0$

Step 3

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

$- x y^{2} + 2 y^{2} = 0$

Step 4

Solve for $x$ .

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Step 4.1

Subtract $2 y^{2}$ from both sides of the equation.

$- x y^{2} = - 2 y^{2}$

Step 4.2

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

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Step 4.2.1

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

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

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Dividing two negative values results in a positive value.

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

Step 4.2.2.2

Cancel the common factor of $y^{2}$ .

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Step 4.2.2.2.1

Cancel the common factor.

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

Step 4.2.2.2.2

Divide $x$ by $1$ .

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

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Cancel the common factor of $y^{2}$ .

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Step 4.2.3.1.1

Cancel the common factor.

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

Step 4.2.3.1.2

Rewrite the expression.

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

Step 4.2.3.1.3

Move the negative one from the denominator of $\frac{- 2}{- 1}$ .

$x = - 1 \cdot - 2$

Step 4.2.3.2

Simplify the expression.

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Step 4.2.3.2.1

Rewrite $- 1 \cdot - 2$ as $- - 2$ .

$x = - - 2$

Step 4.2.3.2.2

Multiply $- 1$ by $- 2$ .

$x = 2$

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 $0$ .

$x = 0, x = 2$

Step 6