Algebra Examples

$a = \frac{1}{2} (b + B) h$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot ((b + B) h) = a$ .

$\frac{1}{2} \cdot ((b + B) h) = a$

Step 2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot ((b + B) h)) = 2 a$

Step 3

Simplify the left side.

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Step 3.1

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

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Step 3.1.1

Apply the distributive property.

$2 (\frac{1}{2} \cdot (b h + B h)) = 2 a$

Step 3.1.2

Apply the distributive property.

$2 (\frac{1}{2} (b h) + \frac{1}{2} (B h)) = 2 a$

Step 3.1.3

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

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Step 3.1.3.1

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

$2 (\frac{b}{2} h + \frac{1}{2} (B h)) = 2 a$

Step 3.1.3.2

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

$2 (\frac{b h}{2} + \frac{1}{2} (B h)) = 2 a$

$2 (\frac{b h}{2} + \frac{1}{2} (B h)) = 2 a$

Step 3.1.4

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

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Step 3.1.4.1

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

$2 (\frac{b h}{2} + \frac{B}{2} h) = 2 a$

Step 3.1.4.2

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

$2 (\frac{b h}{2} + \frac{B h}{2}) = 2 a$

$2 (\frac{b h}{2} + \frac{B h}{2}) = 2 a$

Step 3.1.5

Apply the distributive property.

$2 \frac{b h}{2} + 2 \frac{B h}{2} = 2 a$

Step 3.1.6

Cancel the common factor of $2$ .

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Step 3.1.6.1

Cancel the common factor.

$2 \frac{b h}{2} + 2 \frac{B h}{2} = 2 a$

Step 3.1.6.2

Rewrite the expression.

$b h + 2 \frac{B h}{2} = 2 a$

$b h + 2 \frac{B h}{2} = 2 a$

Step 3.1.7

Cancel the common factor of $2$ .

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Step 3.1.7.1

Cancel the common factor.

$b h + 2 \frac{B h}{2} = 2 a$

Step 3.1.7.2

Rewrite the expression.

$b h + B h = 2 a$

$b h + B h = 2 a$

$b h + B h = 2 a$

$b h + B h = 2 a$

Step 4

Subtract $b h$ from both sides of the equation.

$B h = 2 a - b h$

Step 5

Divide each term in $B h = 2 a - b h$ by $h$ and simplify.

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Step 5.1

Divide each term in $B h = 2 a - b h$ by $h$ .

$\frac{B h}{h} = \frac{2 a}{h} + \frac{- b h}{h}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $h$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{B h}{h} = \frac{2 a}{h} + \frac{- b h}{h}$

Step 5.2.1.2

Divide $B$ by $1$ .

$B = \frac{2 a}{h} + \frac{- b h}{h}$

$B = \frac{2 a}{h} + \frac{- b h}{h}$

$B = \frac{2 a}{h} + \frac{- b h}{h}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $h$ .

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Step 5.3.1.1

Cancel the common factor.

$B = \frac{2 a}{h} + \frac{- b h}{h}$

Step 5.3.1.2

Divide $- b$ by $1$ .

$B = \frac{2 a}{h} - b$

$B = \frac{2 a}{h} - b$

$B = \frac{2 a}{h} - b$

$B = \frac{2 a}{h} - b$

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