Algebra 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.

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