Algebra Examples

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

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

Step 1

Rewrite the equation as

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

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

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

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

Step 2

Multiply both sides of the equation by

2

$2$ .

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

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

Step 3

Simplify the left side.

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Step 3.1

Simplify

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

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

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Step 3.1.1

Apply the distributive property.

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

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

Step 3.1.2

Apply the distributive property.

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

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

Step 3.1.3

Multiply

\frac{1}{2} (h b)

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

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Step 3.1.3.1

Combine

h

$h$ and

\frac{1}{2}

$\frac{1}{2}$ .

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

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

Step 3.1.3.2

Combine

\frac{h}{2}

$\frac{h}{2}$ and

b

$b$ .

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

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

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

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

Step 3.1.4

Multiply

\frac{1}{2} (h B)

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

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Step 3.1.4.1

Combine

h

$h$ and

\frac{1}{2}

$\frac{1}{2}$ .

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

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

Step 3.1.4.2

Combine

\frac{h}{2}

$\frac{h}{2}$ and

B

$B$ .

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

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

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

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

Step 3.1.5

Apply the distributive property.

2 \frac{h b}{2} + 2 \frac{h B}{2} = 2 A

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

Step 3.1.6

Cancel the common factor of

2

$2$ .

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Step 3.1.6.1

Cancel the common factor.

2 \frac{h b}{2} + 2 \frac{h B}{2} = 2 A

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

Step 3.1.6.2

Rewrite the expression.

h b + 2 \frac{h B}{2} = 2 A

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

h b + 2 \frac{h B}{2} = 2 A

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

Step 3.1.7

Cancel the common factor of

2

$2$ .

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Step 3.1.7.1

Cancel the common factor.

h b + 2 \frac{h B}{2} = 2 A

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

Step 3.1.7.2

Rewrite the expression.

h b + h B = 2 A

$h b + h B = 2 A$

h b + h B = 2 A

$h b + h B = 2 A$

h b + h B = 2 A

$h b + h B = 2 A$

h b + h B = 2 A

$h b + h B = 2 A$

Step 4

Factor

h

$h$ out of

h b + h B

$h b + h B$ .

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Step 4.1

Factor

h

$h$ out of

h b

$h b$ .

h (b) + h B = 2 A

$h (b) + h B = 2 A$

Step 4.2

Factor

h

$h$ out of

h B

$h B$ .

h (b) + h (B) = 2 A

$h (b) + h (B) = 2 A$

Step 4.3

Factor

h

$h$ out of

h (b) + h (B)

$h (b) + h (B)$ .

h (b + B) = 2 A

$h (b + B) = 2 A$

h (b + B) = 2 A

$h (b + B) = 2 A$

Step 5

Divide each term in

h (b + B) = 2 A

$h (b + B) = 2 A$ by

b + B

$b + B$ and simplify.

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Step 5.1

Divide each term in

h (b + B) = 2 A

$h (b + B) = 2 A$ by

b + B

$b + B$ .

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

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

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of

b + B

$b + B$ .

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Step 5.2.1.1

Cancel the common factor.

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

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

Step 5.2.1.2

Divide

h

$h$ by

1

$1$ .

h = \frac{2 A}{b + B}

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

h = \frac{2 A}{b + B}

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

h = \frac{2 A}{b + B}

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

h = \frac{2 A}{b + B}

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

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

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