Basic Math Examples

$A = 2 H W + 2 L W + 2 L H$

Step 1

Rewrite the equation as $2 H W + 2 L W + 2 L H = A$ .

$2 H W + 2 L W + 2 L H = A$

Step 2

Subtract $2 L H$ from both sides of the equation.

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

Step 3

Factor $2 W$ out of $2 H W + 2 L W$ .

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Step 3.1

Factor $2 W$ out of $2 H W$ .

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

Step 3.2

Factor $2 W$ out of $2 L W$ .

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

Step 3.3

Factor $2 W$ out of $2 W (H) + 2 W (L)$ .

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

Step 4

Divide each term in $2 W (H + L) = A - 2 L H$ by $2 (H + L)$ and simplify.

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Step 4.1

Divide each term in $2 W (H + L) = A - 2 L H$ by $2 (H + L)$ .

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

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.

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

Step 4.2.1.2

Rewrite the expression.

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

Step 4.2.2

Cancel the common factor of $H + L$ .

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Step 4.2.2.1

Cancel the common factor.

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

Step 4.2.2.2

Divide $W$ by $1$ .

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

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 $- 2 L H$ .

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

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.

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

Step 4.3.1.1.2.2

Rewrite the expression.

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

Step 4.3.1.2

Move the negative in front of the fraction.

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

Step 4.3.2

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

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

Step 4.3.3

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

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Step 4.3.3.1

Multiply $\frac{L H}{H + L}$ by $\frac{2}{2}$ .

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

Step 4.3.3.2

Reorder the factors of $(H + L) \cdot 2$ .

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

Step 4.3.4

Combine the numerators over the common denominator.

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

Step 4.3.5

Multiply $2$ by $- 1$ .

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