Pre-Algebra Examples

$W = 2 X y + 2 X Z + 2 y Z$

Step 1

Rewrite the equation as $2 X y + 2 X Z + 2 y Z = W$ .

$2 X y + 2 X Z + 2 y Z = W$

Step 2

Subtract $2 X y$ from both sides of the equation.

$2 X Z + 2 y Z = W - 2 X y$

Step 3

Factor $2 Z$ out of $2 X Z + 2 y Z$ .

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Step 3.1

Factor $2 Z$ out of $2 X Z$ .

$2 Z (X) + 2 y Z = W - 2 X y$

Step 3.2

Factor $2 Z$ out of $2 y Z$ .

$2 Z (X) + 2 Z (y) = W - 2 X y$

Step 3.3

Factor $2 Z$ out of $2 Z (X) + 2 Z (y)$ .

$2 Z (X + y) = W - 2 X y$

Step 4

Divide each term in $2 Z (X + y) = W - 2 X y$ by $2 (X + y)$ and simplify.

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Step 4.1

Divide each term in $2 Z (X + y) = W - 2 X y$ by $2 (X + y)$ .

$\frac{2 Z (X + y)}{2 (X + y)} = \frac{W}{2 (X + y)} + \frac{- 2 X y}{2 (X + y)}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 Z (X + y)}{2 (X + y)} = \frac{W}{2 (X + y)} + \frac{- 2 X y}{2 (X + y)}$

Step 4.2.1.2

Rewrite the expression.

$\frac{Z (X + y)}{X + y} = \frac{W}{2 (X + y)} + \frac{- 2 X y}{2 (X + y)}$

Step 4.2.2

Cancel the common factor of $X + y$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{Z (X + y)}{X + y} = \frac{W}{2 (X + y)} + \frac{- 2 X y}{2 (X + y)}$

Step 4.2.2.2

Divide $Z$ by $1$ .

$Z = \frac{W}{2 (X + y)} + \frac{- 2 X y}{2 (X + y)}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Cancel the common factor of $- 2$ and $2$ .

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Step 4.3.1.1.1

Factor $2$ out of $- 2 X y$ .

$Z = \frac{W}{2 (X + y)} + \frac{2 (- X y)}{2 (X + y)}$

Step 4.3.1.1.2

Cancel the common factors.

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Step 4.3.1.1.2.1

Cancel the common factor.

$Z = \frac{W}{2 (X + y)} + \frac{2 (- X y)}{2 (X + y)}$

Step 4.3.1.1.2.2

Rewrite the expression.

$Z = \frac{W}{2 (X + y)} + \frac{- X y}{X + y}$

Step 4.3.1.2

Move the negative in front of the fraction.

$Z = \frac{W}{2 (X + y)} - \frac{X y}{X + y}$

Step 4.3.2

To write $- \frac{X y}{X + y}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$Z = \frac{W}{2 (X + y)} - \frac{X y}{X + y} \cdot \frac{2}{2}$

Step 4.3.3

Write each expression with a common denominator of $2 (X + y)$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.3.3.1

Multiply $\frac{X y}{X + y}$ by $\frac{2}{2}$ .

$Z = \frac{W}{2 (X + y)} - \frac{X y \cdot 2}{(X + y) \cdot 2}$

Step 4.3.3.2

Reorder the factors of $(X + y) \cdot 2$ .

$Z = \frac{W}{2 (X + y)} - \frac{X y \cdot 2}{2 (X + y)}$

Step 4.3.4

Combine the numerators over the common denominator.

$Z = \frac{W - X y \cdot 2}{2 (X + y)}$

Step 4.3.5

Multiply $2$ by $- 1$ .

$Z = \frac{W - 2 X y}{2 (X + y)}$