Precalculus Examples

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

Step 1

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

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

Step 2

Multiply both sides of the equation by $2$ .

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

Step 3

Simplify the left side.

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Step 3.1

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

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Step 3.1.1

Apply the distributive property.

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

Step 3.1.2

Apply the distributive property.

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

Step 3.1.3

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

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Step 3.1.3.1

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

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

Step 3.1.3.2

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

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

Step 3.1.4

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

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Step 3.1.4.1

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

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

Step 3.1.4.2

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

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

Step 3.1.5

Apply the distributive property.

$2 \frac{b_{1} h}{2} + 2 \frac{b_{2} h}{2} = 2 A$

Step 3.1.6

Cancel the common factor of $2$ .

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Step 3.1.6.1

Cancel the common factor.

$2 \frac{b_{1} h}{2} + 2 \frac{b_{2} h}{2} = 2 A$

Step 3.1.6.2

Rewrite the expression.

$b_{1} h + 2 \frac{b_{2} h}{2} = 2 A$

Step 3.1.7

Cancel the common factor of $2$ .

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Step 3.1.7.1

Cancel the common factor.

$b_{1} h + 2 \frac{b_{2} h}{2} = 2 A$

Step 3.1.7.2

Rewrite the expression.

$b_{1} h + b_{2} h = 2 A$

Step 4

Factor $h$ out of $b_{1} h + b_{2} h$ .

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Step 4.1

Factor $h$ out of $b_{1} h$ .

$h b_{1} + b_{2} h = 2 A$

Step 4.2

Factor $h$ out of $b_{2} h$ .

$h b_{1} + h b_{2} = 2 A$

Step 4.3

Factor $h$ out of $h b_{1} + h b_{2}$ .

$h (b_{1} + b_{2}) = 2 A$

Step 5

Divide each term in $h (b_{1} + b_{2}) = 2 A$ by $b_{1} + b_{2}$ and simplify.

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Step 5.1

Divide each term in $h (b_{1} + b_{2}) = 2 A$ by $b_{1} + b_{2}$ .

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

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $b_{1} + b_{2}$ .

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Step 5.2.1.1

Cancel the common factor.

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

Step 5.2.1.2

Divide $h$ by $1$ .

$h = \frac{2 A}{b_{1} + b_{2}}$