Basic Math Examples

$s = \frac{r L - a}{b - a}$

Step 1

Rewrite the equation as $\frac{r L - a}{b - a} = s$ .

$\frac{r L - a}{b - a} = s$

Step 2

Multiply both sides by $b - a$ .

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

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $b - a$ .

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Step 3.1.1.1

Cancel the common factor.

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

Step 3.1.1.2

Rewrite the expression.

$r L - a = s (b - a)$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $s (b - a)$ .

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Step 3.2.1.1

Apply the distributive property.

$r L - a = s b + s (- a)$

Step 3.2.1.2

Simplify the expression.

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Step 3.2.1.2.1

Rewrite using the commutative property of multiplication.

$r L - a = s b - s a$

Step 3.2.1.2.2

Reorder $s$ and $b$ .

$r L - a = b s - s a$

Step 3.2.1.2.3

Move $s$ .

$r L - a = b s - a s$

Step 3.2.1.2.4

Reorder $b s$ and $- a s$ .

$r L - a = - a s + b s$

Step 4

Solve for $r$ .

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Step 4.1

Add $a$ to both sides of the equation.

$r L = - a s + b s + a$

Step 4.2

Divide each term in $r L = - a s + b s + a$ by $L$ and simplify.

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Step 4.2.1

Divide each term in $r L = - a s + b s + a$ by $L$ .

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

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $L$ .

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Step 4.2.2.1.1

Cancel the common factor.

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

Step 4.2.2.1.2

Divide $r$ by $1$ .

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

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Move the negative in front of the fraction.

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