Algebra Examples

$V = C (1 - \frac{n}{N})$

Step 1

Rewrite the equation as $C (1 - \frac{n}{N}) = V$ .

$C (1 - \frac{n}{N}) = V$

Step 2

Divide each term in $C (1 - \frac{n}{N}) = V$ by $C$ and simplify.

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Step 2.1

Divide each term in $C (1 - \frac{n}{N}) = V$ by $C$ .

$\frac{C (1 - \frac{n}{N})}{C} = \frac{V}{C}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $C$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{C (1 - \frac{n}{N})}{C} = \frac{V}{C}$

Step 2.2.1.2

Divide $1 - \frac{n}{N}$ by $1$ .

$1 - \frac{n}{N} = \frac{V}{C}$

Step 3

Subtract $\frac{V}{C}$ from both sides of the equation.

$1 - \frac{n}{N} - \frac{V}{C} = 0$

Step 4

Move all terms not containing $n$ to the right side of the equation.

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Step 4.1

Subtract $1$ from both sides of the equation.

$- \frac{n}{N} - \frac{V}{C} = - 1$

Step 4.2

Add $\frac{V}{C}$ to both sides of the equation.

$- \frac{n}{N} = - 1 + \frac{V}{C}$

Step 5

Divide each term in $- \frac{n}{N} = - 1 + \frac{V}{C}$ by $- 1$ and simplify.

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Step 5.1

Divide each term in $- \frac{n}{N} = - 1 + \frac{V}{C}$ by $- 1$ .

$\frac{- \frac{n}{N}}{- 1} = \frac{- 1}{- 1} + \frac{\frac{V}{C}}{- 1}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Dividing two negative values results in a positive value.

$\frac{\frac{n}{N}}{1} = \frac{- 1}{- 1} + \frac{\frac{V}{C}}{- 1}$

Step 5.2.2

Divide $\frac{n}{N}$ by $1$ .

$\frac{n}{N} = \frac{- 1}{- 1} + \frac{\frac{V}{C}}{- 1}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Simplify each term.

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Step 5.3.1.1

Divide $- 1$ by $- 1$ .

$\frac{n}{N} = 1 + \frac{\frac{V}{C}}{- 1}$

Step 5.3.1.2

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

$\frac{n}{N} = 1 - 1 \cdot \frac{V}{C}$

Step 5.3.1.3

Rewrite $- 1 \cdot \frac{V}{C}$ as $- \frac{V}{C}$ .

$\frac{n}{N} = 1 - \frac{V}{C}$

Step 6

Multiply both sides by $N$ .

$\frac{n}{N} N = (1 - \frac{V}{C}) N$

Step 7

Simplify.

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Step 7.1

Simplify the left side.

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Step 7.1.1

Cancel the common factor of $N$ .

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Step 7.1.1.1

Cancel the common factor.

$\frac{n}{N} N = (1 - \frac{V}{C}) N$

Step 7.1.1.2

Rewrite the expression.

$n = (1 - \frac{V}{C}) N$

Step 7.2

Simplify the right side.

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Step 7.2.1

Simplify $(1 - \frac{V}{C}) N$ .

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Step 7.2.1.1

Apply the distributive property.

$n = 1 N - \frac{V}{C} N$

Step 7.2.1.2

Multiply $N$ by $1$ .

$n = N - \frac{V}{C} N$

Step 7.2.1.3

Combine $N$ and $\frac{V}{C}$ .

$n = N - \frac{N V}{C}$

Step 7.2.1.4

Reorder $N$ and $- \frac{N V}{C}$ .

$n = - \frac{N V}{C} + N$