Basic Math Examples

$s = \frac{w - d}{z - g}$

Step 1

Rewrite the equation as $\frac{w - d}{z - g} = s$ .

$\frac{w - d}{z - g} = s$

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.

$z - g, 1$

Step 2.2

Remove parentheses.

$z - g, 1$

Step 2.3

The LCM of one and any expression is the expression.

$z - g$

Step 3

Multiply each term in $\frac{w - d}{z - g} = s$ by $z - g$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{w - d}{z - g} = s$ by $z - g$ .

$\frac{w - d}{z - g} (z - g) = s (z - g)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $z - g$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{w - d}{z - g} (z - g) = s (z - g)$

Step 3.2.1.2

Rewrite the expression.

$w - d = s (z - g)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$w - d = s z + s (- g)$

Step 3.3.2

Rewrite using the commutative property of multiplication.

$w - d = s z - s g$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $s z - s g = w - d$ .

$s z - s g = w - d$

Step 4.2

Subtract $s z$ from both sides of the equation.

$- s g = w - d - s z$

Step 4.3

Divide each term in $- s g = w - d - s z$ by $- s$ and simplify.

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Step 4.3.1

Divide each term in $- s g = w - d - s z$ by $- s$ .

$\frac{- s g}{- s} = \frac{w}{- s} + \frac{- d}{- s} + \frac{- s z}{- s}$

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.

$\frac{s g}{s} = \frac{w}{- s} + \frac{- d}{- s} + \frac{- s z}{- s}$

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.

$\frac{s g}{s} = \frac{w}{- s} + \frac{- d}{- s} + \frac{- s z}{- s}$

Step 4.3.2.2.2

Divide $g$ by $1$ .

$g = \frac{w}{- s} + \frac{- d}{- s} + \frac{- s z}{- s}$

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.

$g = - \frac{w}{s} + \frac{- d}{- s} + \frac{- s z}{- s}$

Step 4.3.3.1.2

Dividing two negative values results in a positive value.

$g = - \frac{w}{s} + \frac{d}{s} + \frac{- s z}{- s}$

Step 4.3.3.1.3

Dividing two negative values results in a positive value.

$g = - \frac{w}{s} + \frac{d}{s} + \frac{s z}{s}$

Step 4.3.3.1.4

Cancel the common factor of $s$ .

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Step 4.3.3.1.4.1

Cancel the common factor.

$g = - \frac{w}{s} + \frac{d}{s} + \frac{s z}{s}$

Step 4.3.3.1.4.2

Divide $z$ by $1$ .

$g = - \frac{w}{s} + \frac{d}{s} + z$