Finite Math Examples

$R = (\frac{e}{v}) \cdot r + (\frac{d}{v}) \cdot L$

Step 1

Rewrite the equation as $\frac{e}{v} \cdot r + \frac{d}{v} \cdot L = R$ .

$\frac{e}{v} \cdot r + \frac{d}{v} \cdot L = R$

Step 2

Simplify each term.

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Step 2.1

Combine $\frac{e}{v}$ and $r$ .

$\frac{e r}{v} + \frac{d}{v} \cdot L = R$

Step 2.2

Combine $\frac{d}{v}$ and $L$ .

$\frac{e r}{v} + \frac{d L}{v} = R$

Step 3

Subtract $\frac{d L}{v}$ from both sides of the equation.

$\frac{e r}{v} = R - \frac{d L}{v}$

Step 4

Multiply both sides by $v$ .

$\frac{e r}{v} v = (R - \frac{d L}{v}) v$

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $v$ .

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Step 5.1.1.1

Cancel the common factor.

$\frac{e r}{v} v = (R - \frac{d L}{v}) v$

Step 5.1.1.2

Rewrite the expression.

$e r = (R - \frac{d L}{v}) v$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $(R - \frac{d L}{v}) v$ .

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Step 5.2.1.1

Apply the distributive property.

$e r = R v - \frac{d L}{v} v$

Step 5.2.1.2

Cancel the common factor of $v$ .

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Step 5.2.1.2.1

Move the leading negative in $- \frac{d L}{v}$ into the numerator.

$e r = R v + \frac{- d L}{v} v$

Step 5.2.1.2.2

Cancel the common factor.

$e r = R v + \frac{- d L}{v} v$

Step 5.2.1.2.3

Rewrite the expression.

$e r = R v - d L$

Step 5.2.1.3

Simplify with commuting.

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Step 5.2.1.3.1

Reorder $R$ and $v$ .

$e r = v R - d L$

Step 5.2.1.3.2

Reorder $v R$ and $- d L$ .

$e r = - d L + v R$

Step 6

Divide each term in $e r = - d L + v R$ by $e$ and simplify.

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Step 6.1

Divide each term in $e r = - d L + v R$ by $e$ .

$\frac{e r}{e} = \frac{- d L}{e} + \frac{v R}{e}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $e$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{e r}{e} = \frac{- d L}{e} + \frac{v R}{e}$

Step 6.2.1.2

Divide $r$ by $1$ .

$r = \frac{- d L}{e} + \frac{v R}{e}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Move the negative in front of the fraction.

$r = - \frac{d L}{e} + \frac{v R}{e}$