Precalculus Examples

$s = 2 l w + 2 h w + 2 h l$

Step 1

Rewrite the equation as $2 l w + 2 h w + 2 h l = s$ .

$2 l w + 2 h w + 2 h l = s$

Step 2

Subtract $2 h l$ from both sides of the equation.

$2 l w + 2 h w = s - 2 h l$

Step 3

Factor $2 w$ out of $2 l w + 2 h w$ .

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Step 3.1

Factor $2 w$ out of $2 l w$ .

$2 w (l) + 2 h w = s - 2 h l$

Step 3.2

Factor $2 w$ out of $2 h w$ .

$2 w (l) + 2 w (h) = s - 2 h l$

Step 3.3

Factor $2 w$ out of $2 w (l) + 2 w (h)$ .

$2 w (l + h) = s - 2 h l$

Step 4

Divide each term in $2 w (l + h) = s - 2 h l$ by $2 (l + h)$ and simplify.

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Step 4.1

Divide each term in $2 w (l + h) = s - 2 h l$ by $2 (l + h)$ .

$\frac{2 w (l + h)}{2 (l + h)} = \frac{s}{2 (l + h)} + \frac{- 2 h l}{2 (l + h)}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 w (l + h)}{2 (l + h)} = \frac{s}{2 (l + h)} + \frac{- 2 h l}{2 (l + h)}$

Step 4.2.1.2

Rewrite the expression.

$\frac{w (l + h)}{l + h} = \frac{s}{2 (l + h)} + \frac{- 2 h l}{2 (l + h)}$

Step 4.2.2

Cancel the common factor of $l + h$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{w (l + h)}{l + h} = \frac{s}{2 (l + h)} + \frac{- 2 h l}{2 (l + h)}$

Step 4.2.2.2

Divide $w$ by $1$ .

$w = \frac{s}{2 (l + h)} + \frac{- 2 h l}{2 (l + h)}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Cancel the common factor of $- 2$ and $2$ .

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Step 4.3.1.1.1

Factor $2$ out of $- 2 h l$ .

$w = \frac{s}{2 (l + h)} + \frac{2 (- h l)}{2 (l + h)}$

Step 4.3.1.1.2

Cancel the common factors.

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Step 4.3.1.1.2.1

Cancel the common factor.

$w = \frac{s}{2 (l + h)} + \frac{2 (- h l)}{2 (l + h)}$

Step 4.3.1.1.2.2

Rewrite the expression.

$w = \frac{s}{2 (l + h)} + \frac{- h l}{l + h}$

Step 4.3.1.2

Move the negative in front of the fraction.

$w = \frac{s}{2 (l + h)} - \frac{h l}{l + h}$

Step 4.3.2

To write $- \frac{h l}{l + h}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$w = \frac{s}{2 (l + h)} - \frac{h l}{l + h} \cdot \frac{2}{2}$

Step 4.3.3

Write each expression with a common denominator of $2 (l + h)$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.3.3.1

Multiply $\frac{h l}{l + h}$ by $\frac{2}{2}$ .

$w = \frac{s}{2 (l + h)} - \frac{h l \cdot 2}{(l + h) \cdot 2}$

Step 4.3.3.2

Reorder the factors of $(l + h) \cdot 2$ .

$w = \frac{s}{2 (l + h)} - \frac{h l \cdot 2}{2 (l + h)}$

Step 4.3.4

Combine the numerators over the common denominator.

$w = \frac{s - h l \cdot 2}{2 (l + h)}$

Step 4.3.5

Multiply $2$ by $- 1$ .

$w = \frac{s - 2 h l}{2 (l + h)}$