Algebra Examples

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

Step 1

Simplify $\frac{a + b}{2} \cdot h$ .

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Step 1.1

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

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

Step 1.2

Reorder factors in $\frac{(a + b) h}{2}$ .

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

Step 2

Move all terms containing $a$ to the left side of the equation.

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Step 2.1

Subtract $\frac{h (a + b)}{2}$ from both sides of the equation.

$a - \frac{h (a + b)}{2} = 0$

Step 2.2

To write $a$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$a \cdot \frac{2}{2} - \frac{h (a + b)}{2} = 0$

Step 2.3

Combine $a$ and $\frac{2}{2}$ .

$\frac{a \cdot 2}{2} - \frac{h (a + b)}{2} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{a \cdot 2 - h (a + b)}{2} = 0$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Move $2$ to the left of $a$ .

$\frac{2 \cdot a - h (a + b)}{2} = 0$

Step 2.5.2

Apply the distributive property.

$\frac{2 a - h a - h b}{2} = 0$

Step 3

Set the numerator equal to zero.

$2 a - h a - h b = 0$

Step 4

Solve the equation for $a$ .

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Step 4.1

Add $h b$ to both sides of the equation.

$2 a - h a = h b$

Step 4.2

Factor $a$ out of $2 a - h a$ .

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Step 4.2.1

Factor $a$ out of $2 a$ .

$a \cdot 2 - h a = h b$

Step 4.2.2

Factor $a$ out of $- h a$ .

$a \cdot 2 + a (- h) = h b$

Step 4.2.3

Factor $a$ out of $a \cdot 2 + a (- h)$ .

$a (2 - h) = h b$

Step 4.3

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

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Step 4.3.1

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

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

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $2 - h$ .

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Step 4.3.2.1.1

Cancel the common factor.

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

Step 4.3.2.1.2

Divide $a$ by $1$ .

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