Algebra Examples

s = 2 L W + 2 L H + 2 W H

$s = 2 L W + 2 L H + 2 W H$

Step 1

Rewrite the equation as

2 L W + 2 L H + 2 W H = s

$2 L W + 2 L H + 2 W H = s$ .

2 L W + 2 L H + 2 W H = s

$2 L W + 2 L H + 2 W H = s$

Step 2

Subtract

2 L W

$2 L W$ from both sides of the equation.

2 L H + 2 W H = s - 2 L W

$2 L H + 2 W H = s - 2 L W$

Step 3

Factor

2 H

$2 H$ out of

2 L H + 2 W H

$2 L H + 2 W H$ .

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Step 3.1

Factor

2 H

$2 H$ out of

2 L H

$2 L H$ .

2 H (L) + 2 W H = s - 2 L W

$2 H (L) + 2 W H = s - 2 L W$

Step 3.2

Factor

2 H

$2 H$ out of

2 W H

$2 W H$ .

2 H (L) + 2 H (W) = s - 2 L W

$2 H (L) + 2 H (W) = s - 2 L W$

Step 3.3

Factor

2 H

$2 H$ out of

2 H (L) + 2 H (W)

$2 H (L) + 2 H (W)$ .

2 H (L + W) = s - 2 L W

$2 H (L + W) = s - 2 L W$

2 H (L + W) = s - 2 L W

$2 H (L + W) = s - 2 L W$

Step 4

Divide each term in

2 H (L + W) = s - 2 L W

$2 H (L + W) = s - 2 L W$ by

2 (L + W)

$2 (L + W)$ and simplify.

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Step 4.1

Divide each term in

2 H (L + W) = s - 2 L W

$2 H (L + W) = s - 2 L W$ by

2 (L + W)

$2 (L + W)$ .

\frac{2 H (L + W)}{2 (L + W)} = \frac{s}{2 (L + W)} + \frac{- 2 L W}{2 (L + W)}

$\frac{2 H (L + W)}{2 (L + W)} = \frac{s}{2 (L + W)} + \frac{- 2 L W}{2 (L + W)}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of

2

$2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 H (L + W)}{2 (L + W)} = \frac{s}{2 (L + W)} + \frac{- 2 L W}{2 (L + W)}$

Step 4.2.1.2

Rewrite the expression.

$\frac{H (L + W)}{L + W} = \frac{s}{2 (L + W)} + \frac{- 2 L W}{2 (L + W)}$

Step 4.2.2

Cancel the common factor of

$L + W$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{H (L + W)}{L + W} = \frac{s}{2 (L + W)} + \frac{- 2 L W}{2 (L + W)}$

Step 4.2.2.2

Divide

$H$ by

$1$ .

$H = \frac{s}{2 (L + W)} + \frac{- 2 L W}{2 (L + W)}$

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

$- 2 L W$ .

$H = \frac{s}{2 (L + W)} + \frac{2 (- L W)}{2 (L + W)}$

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.

$H = \frac{s}{2 (L + W)} + \frac{2 (- L W)}{2 (L + W)}$

Step 4.3.1.1.2.2

Rewrite the expression.

$H = \frac{s}{2 (L + W)} + \frac{- L W}{L + W}$

Step 4.3.1.2

Move the negative in front of the fraction.

$H = \frac{s}{2 (L + W)} - \frac{L W}{L + W}$

Step 4.3.2

To write

$- \frac{L W}{L + W}$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$H = \frac{s}{2 (L + W)} - \frac{L W}{L + W} \cdot \frac{2}{2}$

Step 4.3.3

Write each expression with a common denominator of

$2 (L + W)$ , by multiplying each by an appropriate factor of

$1$ .

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Step 4.3.3.1

Multiply

$\frac{L W}{L + W}$ by

$\frac{2}{2}$ .

$H = \frac{s}{2 (L + W)} - \frac{L W \cdot 2}{(L + W) \cdot 2}$

Step 4.3.3.2

Reorder the factors of

$(L + W) \cdot 2$ .

$H = \frac{s}{2 (L + W)} - \frac{L W \cdot 2}{2 (L + W)}$

Step 4.3.4

Combine the numerators over the common denominator.

$H = \frac{s - L W \cdot 2}{2 (L + W)}$

Step 4.3.5

Multiply

$2$ by

$- 1$ .

$H = \frac{s - 2 L W}{2 (L + W)}$