Precalculus Examples

$S = \frac{a}{1 - r}$

Step 1

Rewrite the equation as $\frac{a}{1 - r} = S$ .

$\frac{a}{1 - r} = S$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$1 - r, 1$

Step 2.2

Remove parentheses.

$1 - r, 1$

Step 2.3

The LCM of one and any expression is the expression.

$1 - r$

Step 3

Multiply each term in $\frac{a}{1 - r} = S$ by $1 - r$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{a}{1 - r} = S$ by $1 - r$ .

$\frac{a}{1 - r} (1 - r) = S (1 - r)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $1 - r$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{a}{1 - r} (1 - r) = S (1 - r)$

Step 3.2.1.2

Rewrite the expression.

$a = S (1 - r)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$a = S \cdot 1 + S (- r)$

Step 3.3.2

Simplify the expression.

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Step 3.3.2.1

Multiply $S$ by $1$ .

$a = S + S (- r)$

Step 3.3.2.2

Rewrite using the commutative property of multiplication.

$a = S - S r$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $S - S r = a$ .

$S - S r = a$

Step 4.2

Subtract $S$ from both sides of the equation.

$- S r = a - S$

Step 4.3

Divide each term in $- S r = a - S$ by $- S$ and simplify.

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Step 4.3.1

Divide each term in $- S r = a - S$ by $- S$ .

$\frac{- S r}{- S} = \frac{a}{- S} + \frac{- S}{- S}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Dividing two negative values results in a positive value.

$\frac{S r}{S} = \frac{a}{- S} + \frac{- S}{- S}$

Step 4.3.2.2

Cancel the common factor of $S$ .

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Step 4.3.2.2.1

Cancel the common factor.

$\frac{S r}{S} = \frac{a}{- S} + \frac{- S}{- S}$

Step 4.3.2.2.2

Divide $r$ by $1$ .

$r = \frac{a}{- S} + \frac{- S}{- S}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Simplify each term.

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Step 4.3.3.1.1

Move the negative in front of the fraction.

$r = - \frac{a}{S} + \frac{- S}{- S}$

Step 4.3.3.1.2

Dividing two negative values results in a positive value.

$r = - \frac{a}{S} + \frac{S}{S}$

Step 4.3.3.1.3

Cancel the common factor of $S$ .

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Step 4.3.3.1.3.1

Cancel the common factor.

$r = - \frac{a}{S} + \frac{S}{S}$

Step 4.3.3.1.3.2

Rewrite the expression.

$r = - \frac{a}{S} + 1$