Basic Math Examples

$D = (\frac{G + S e}{1 + e}) W$

Step 1

Rewrite the equation as $\frac{G + S e}{1 + e} \cdot W = D$ .

$\frac{G + S e}{1 + e} \cdot W = D$

Step 2

Simplify $\frac{G + S e}{1 + e} \cdot W$ .

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Step 2.1

Combine $\frac{G + S e}{1 + e}$ and $W$ .

$\frac{(G + S e) W}{1 + e} = D$

Step 2.2

Reorder factors in $\frac{(G + S e) W}{1 + e}$ .

$\frac{W (G + S e)}{1 + e} = D$

Step 3

Multiply both sides by $1 + e$ .

$\frac{W (G + S e)}{1 + e} (1 + e) = D (1 + e)$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{W (G + S e)}{1 + e} (1 + e)$ .

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Step 4.1.1.1

Cancel the common factor of $1 + e$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{W (G + S e)}{1 + e} (1 + e) = D (1 + e)$

Step 4.1.1.1.2

Rewrite the expression.

$W (G + S e) = D (1 + e)$

Step 4.1.1.2

Apply the distributive property.

$W G + W (S e) = D (1 + e)$

Step 4.1.1.3

Simplify the expression.

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Step 4.1.1.3.1

Rewrite using the commutative property of multiplication.

$W G + e W S = D (1 + e)$

Step 4.1.1.3.2

Reorder $W$ and $G$ .

$G W + e W S = D (1 + e)$

Step 4.1.1.3.3

Move $e$ .

$G W + W S e = D (1 + e)$

Step 4.1.1.3.4

Reorder $W$ and $S$ .

$G W + S W e = D (1 + e)$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $D (1 + e)$ .

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Step 4.2.1.1

Apply the distributive property.

$G W + S W e = D \cdot 1 + D e$

Step 4.2.1.2

Multiply $D$ by $1$ .

$G W + S W e = D + D e$

Step 5

Solve for $S$ .

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Step 5.1

Subtract $G W$ from both sides of the equation.

$S W e = D + D e - G W$

Step 5.2

Divide each term in $S W e = D + D e - G W$ by $W e$ and simplify.

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Step 5.2.1

Divide each term in $S W e = D + D e - G W$ by $W e$ .

$\frac{S W e}{W e} = \frac{D}{W e} + \frac{D e}{W e} + \frac{- G W}{W e}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $W$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{S W e}{W e} = \frac{D}{W e} + \frac{D e}{W e} + \frac{- G W}{W e}$

Step 5.2.2.1.2

Rewrite the expression.

$\frac{S e}{e} = \frac{D}{W e} + \frac{D e}{W e} + \frac{- G W}{W e}$

Step 5.2.2.2

Cancel the common factor of $e$ .

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Step 5.2.2.2.1

Cancel the common factor.

$\frac{S e}{e} = \frac{D}{W e} + \frac{D e}{W e} + \frac{- G W}{W e}$

Step 5.2.2.2.2

Divide $S$ by $1$ .

$S = \frac{D}{W e} + \frac{D e}{W e} + \frac{- G W}{W e}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Simplify each term.

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Step 5.2.3.1.1

Cancel the common factor of $e$ .

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Step 5.2.3.1.1.1

Cancel the common factor.

$S = \frac{D}{W e} + \frac{D e}{W e} + \frac{- G W}{W e}$

Step 5.2.3.1.1.2

Rewrite the expression.

$S = \frac{D}{W e} + \frac{D}{W} + \frac{- G W}{W e}$

Step 5.2.3.1.2

Cancel the common factor of $W$ .

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Step 5.2.3.1.2.1

Cancel the common factor.

$S = \frac{D}{W e} + \frac{D}{W} + \frac{- G W}{W e}$

Step 5.2.3.1.2.2

Rewrite the expression.

$S = \frac{D}{W e} + \frac{D}{W} + \frac{- G}{e}$

Step 5.2.3.1.3

Move the negative in front of the fraction.

$S = \frac{D}{W e} + \frac{D}{W} - \frac{G}{e}$