Algebra Examples

$A = S (1 - D N)$

Step 1

Rewrite the equation as $S (1 - D N) = A$ .

$S (1 - D N) = A$

Step 2

Divide each term in $S (1 - D N) = A$ by $S$ and simplify.

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Step 2.1

Divide each term in $S (1 - D N) = A$ by $S$ .

$\frac{S (1 - D N)}{S} = \frac{A}{S}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $S$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{S (1 - D N)}{S} = \frac{A}{S}$

Step 2.2.1.2

Divide $1 - D N$ by $1$ .

$1 - D N = \frac{A}{S}$

Step 3

Subtract $1$ from both sides of the equation.

$- D N = \frac{A}{S} - 1$

Step 4

Divide each term in $- D N = \frac{A}{S} - 1$ by $- D$ and simplify.

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Step 4.1

Divide each term in $- D N = \frac{A}{S} - 1$ by $- D$ .

$\frac{- D N}{- D} = \frac{\frac{A}{S}}{- D} + \frac{- 1}{- D}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{D N}{D} = \frac{\frac{A}{S}}{- D} + \frac{- 1}{- D}$

Step 4.2.2

Cancel the common factor of $D$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{D N}{D} = \frac{\frac{A}{S}}{- D} + \frac{- 1}{- D}$

Step 4.2.2.2

Divide $N$ by $1$ .

$N = \frac{\frac{A}{S}}{- D} + \frac{- 1}{- D}$

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

Multiply the numerator by the reciprocal of the denominator.

$N = \frac{A}{S} \cdot \frac{1}{- D} + \frac{- 1}{- D}$

Step 4.3.1.2

Cancel the common factor of $1$ and $- 1$ .

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Step 4.3.1.2.1

Rewrite $1$ as $- 1 (- 1)$ .

$N = \frac{A}{S} \cdot \frac{- 1 (- 1)}{- D} + \frac{- 1}{- D}$

Step 4.3.1.2.2

Move the negative in front of the fraction.

$N = \frac{A}{S} (- \frac{1}{D}) + \frac{- 1}{- D}$

Step 4.3.1.3

Rewrite using the commutative property of multiplication.

$N = - \frac{A}{S} \cdot \frac{1}{D} + \frac{- 1}{- D}$

Step 4.3.1.4

Multiply $\frac{1}{D}$ by $\frac{A}{S}$ .

$N = - \frac{A}{D S} + \frac{- 1}{- D}$

Step 4.3.1.5

Dividing two negative values results in a positive value.

$N = - \frac{A}{D S} + \frac{1}{D}$