Calculus Examples

$a = l w + h w + l h$

Step 1

Rewrite the equation as $l w + h w + l h = a$ .

$l w + h w + l h = a$

Step 2

Subtract $l w$ from both sides of the equation.

$h w + l h = a - l w$

Step 3

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

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Step 3.1

Factor $h$ out of $h w$ .

$h (w) + l h = a - l w$

Step 3.2

Factor $h$ out of $l h$ .

$h (w) + h l = a - l w$

Step 3.3

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

$h (w + l) = a - l w$

Step 4

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

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Step 4.1

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

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $w + l$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $h$ by $1$ .

$h = \frac{a}{w + l} + \frac{- l w}{w + l}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Combine the numerators over the common denominator.

$h = \frac{a - l w}{w + l}$