Algebra Examples

$A = \frac{1}{2} \cdot (h (c + d))$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot (h (c + d)) = A$ .

$\frac{1}{2} \cdot (h (c + d)) = A$

Step 2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (h (c + d))) = 2 A$

Step 3

Simplify the left side.

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Step 3.1

Simplify $2 (\frac{1}{2} \cdot (h (c + d)))$ .

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Step 3.1.1

Apply the distributive property.

$2 (\frac{1}{2} \cdot (h c + h d)) = 2 A$

Step 3.1.2

Apply the distributive property.

$2 (\frac{1}{2} (h c) + \frac{1}{2} (h d)) = 2 A$

Step 3.1.3

Multiply $\frac{1}{2} (h c)$ .

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Step 3.1.3.1

Combine $h$ and $\frac{1}{2}$ .

$2 (\frac{h}{2} c + \frac{1}{2} (h d)) = 2 A$

Step 3.1.3.2

Combine $\frac{h}{2}$ and $c$ .

$2 (\frac{h c}{2} + \frac{1}{2} (h d)) = 2 A$

$2 (\frac{h c}{2} + \frac{1}{2} (h d)) = 2 A$

Step 3.1.4

Multiply $\frac{1}{2} (h d)$ .

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Step 3.1.4.1

Combine $h$ and $\frac{1}{2}$ .

$2 (\frac{h c}{2} + \frac{h}{2} d) = 2 A$

Step 3.1.4.2

Combine $\frac{h}{2}$ and $d$ .

$2 (\frac{h c}{2} + \frac{h d}{2}) = 2 A$

$2 (\frac{h c}{2} + \frac{h d}{2}) = 2 A$

Step 3.1.5

Apply the distributive property.

$2 \frac{h c}{2} + 2 \frac{h d}{2} = 2 A$

Step 3.1.6

Cancel the common factor of $2$ .

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Step 3.1.6.1

Cancel the common factor.

$2 \frac{h c}{2} + 2 \frac{h d}{2} = 2 A$

Step 3.1.6.2

Rewrite the expression.

$h c + 2 \frac{h d}{2} = 2 A$

$h c + 2 \frac{h d}{2} = 2 A$

Step 3.1.7

Cancel the common factor of $2$ .

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Step 3.1.7.1

Cancel the common factor.

$h c + 2 \frac{h d}{2} = 2 A$

Step 3.1.7.2

Rewrite the expression.

$h c + h d = 2 A$

$h c + h d = 2 A$

$h c + h d = 2 A$

$h c + h d = 2 A$

Step 4

Factor $h$ out of $h c + h d$ .

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Step 4.1

Factor $h$ out of $h c$ .

$h (c) + h d = 2 A$

Step 4.2

Factor $h$ out of $h d$ .

$h (c) + h (d) = 2 A$

Step 4.3

Factor $h$ out of $h (c) + h (d)$ .

$h (c + d) = 2 A$

$h (c + d) = 2 A$

Step 5

Divide each term in $h (c + d) = 2 A$ by $c + d$ and simplify.

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Step 5.1

Divide each term in $h (c + d) = 2 A$ by $c + d$ .

$\frac{h (c + d)}{c + d} = \frac{2 A}{c + d}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $c + d$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{h (c + d)}{c + d} = \frac{2 A}{c + d}$

Step 5.2.1.2

Divide $h$ by $1$ .

$h = \frac{2 A}{c + d}$

$h = \frac{2 A}{c + d}$

$h = \frac{2 A}{c + d}$

$h = \frac{2 A}{c + d}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$