Basic Math Examples

$\frac{w - n}{w n} = p$

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

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

$w n, 1$

Step 1.2

The LCM of one and any expression is the expression.

$w n$

Step 2

Multiply each term in $\frac{w - n}{w n} = p$ by $w n$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{w - n}{w n} = p$ by $w n$ .

$\frac{w - n}{w n} (w n) = p (w n)$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $w n$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{w - n}{w n} (w n) = p (w n)$

Step 2.2.1.2

Rewrite the expression.

$w - n = p (w n)$

Step 2.3

Simplify the right side.

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Step 2.3.1

Remove parentheses.

$w - n = p w n$

Step 3

Solve the equation.

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Step 3.1

Subtract $p w n$ from both sides of the equation.

$w - n - p w n = 0$

Step 3.2

Add $n$ to both sides of the equation.

$w - p w n = n$

Step 3.3

Factor $w$ out of $w - p w n$ .

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Step 3.3.1

Factor $w$ out of $w^{1}$ .

$w \cdot 1 - p w n = n$

Step 3.3.2

Factor $w$ out of $- p w n$ .

$w \cdot 1 + w (- p n) = n$

Step 3.3.3

Factor $w$ out of $w \cdot 1 + w (- p n)$ .

$w (1 - p n) = n$

Step 3.4

Divide each term in $w (1 - p n) = n$ by $1 - p n$ and simplify.

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Step 3.4.1

Divide each term in $w (1 - p n) = n$ by $1 - p n$ .

$\frac{w (1 - p n)}{1 - p n} = \frac{n}{1 - p n}$

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $1 - p n$ .

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Step 3.4.2.1.1

Cancel the common factor.

$\frac{w (1 - p n)}{1 - p n} = \frac{n}{1 - p n}$

Step 3.4.2.1.2

Divide $w$ by $1$ .

$w = \frac{n}{1 - p n}$