Solve for r s=a/(1-r)

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

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.

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

$1 - r, 1$

Remove parentheses.

$1 - r, 1$

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.

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

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

Simplify the left side.

Cancel the common factor of $1 - r$ .

Cancel the common factor.

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

Rewrite the expression.

$a = s (1 - r)$

Simplify the right side.

Apply the distributive property.

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

Simplify the expression.

Multiply $s$ by $1$ .

$a = s + s (- r)$

Rewrite using the commutative property of multiplication.

$a = s - s r$

Step 4

Solve the equation.

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

$s - s r = a$

Subtract $s$ from both sides of the equation.

$- s r = a - s$

Divide each term in $- s r = a - s$ by $- 1 s$ and simplify.

Divide each term in $- s r = a - s$ by $- 1 s$ .

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Cancel the common factor of $s$ .

Cancel the common factor.

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

Divide $r$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

Dividing two negative values results in a positive value.

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

Cancel the common factor of $s$ .

Cancel the common factor.

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

Rewrite the expression.

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

Solve for r s=a/(1-r)

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